12) 4c3 (0.4)3(0.96) + 4c4 (0.4)4
Questions from various materials n books : PERMUTATIONS & COMBINATIONS
{ I would continue adding qs in this forum everyday . }
3) There are 2 women participating in a chess tournment. Every participant played 2 games with the other participants. The number of games that the men played between themselves exceeded by 66 as compared to the number of games that the men played with the women. Find the number of participants & the total numbers of games played in the tournament.
5) 5 boys & 4 girls sit in a straight line. Find the number of ways in which they can be seated if 2 girls are together & the other 2 are also together but separate from the first 2.
15) A train going from Cambridge to London stops at nine intermediate stations. 6 persons enter the train during the journey with 6 different tickets of the same class. How many different sets of ticket may they have had?
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33 Answers
4@gsns :
12 ) ANS - 328 / 625 (ur ans is wrong)
15 ) 1/2 (ur ans is correct)
2)97/(25)4 (ur ans wrong )
Try once again & post the entire solution & not just the ans : )
415 ) Winning 2 games = 3C2
P(WIN) = 0.5
P(LOSE or TIE)= 0.5
Winning all 3 ganes = 3C3
Total probability = 3C2(0.5)2(0.5) + 3C3(0.5)3
= 1/2
4@gsns : )
2 ) No.s with product = 18 r 29 , 92 , 63 , 36
The event E should occur atleast 3 times
Hence the ans
4Probability contd....
17) In a batch of 10 articles, 4 articles are defective. 6 articles are taken from the batch for inspection. If more than 2 articles in this batch are defective, the whole batch is rejected. Find the probability that the batch will be rejected.
20) An author writes a good book with a probability of 1/2 . If it is good it is published with a probability of 2/3. If it is not, it is published with a probability of 1/4. Find the probability that he will get atleast one book published if he writes two.
23) Two cards are drawn from a well shuffled pack of 52 cards. Find the probability that one of them is a red card & the other is a queen.
27)Each of the 'n' passengers sitting in a bus may get down from it at next stop with probability P.Moreover, at the next stop either no passenger or exactly one passenger boards the bus. The probability of no passenger boarding the bus at the next stop being Po . Find the probability that when the bus continues on its way after the stop, there will again be 'n' passengers in the bus.
28) An examination consists of 8 questions in each of which the candidate must say which one of the 5 alternatives is correct one. Assuming that the student has not prepared earlier chooses for each of the question any one of 5 answers with equal probability.
1) prove that the probability that he gets more than one answer is (58 - 3 x 48) / 58.
2) Find the probability that he gets correct answers to six or more questions.
3) Find the standard deviation of this distribution.
30) 16 players take part in a tennis tournment. The order of the matches is chosen at random. There is always a player better than another one, the better wins. Find
a) The probability that all the 4 best players reach the semifinals.
b) The probability that the sixth best reaches the semifinals.
4PROBABILITY
2 ) Numbers are selected at random, one at a time, from the two digit numbers 00, 01, 02,....,99 with replacement. An event E occurs if & only if the product of the two digits of a selected number is 18. If four numbers are selected, find the probability that the event E occurs at least 3 times.
3) To pass a test a child has to perform successfully in two consecutive tasks, one easy and one hard task. The easy task he can perform successfully with probability `e` and the hard task he can perform successfully with probability `h`, where h<e. He is allowed 3 attempts, either in the order (easy, hard, easy) (option A) or in the order (hard,easy,hard) (optionB) whatever may be the order, he may be successful twice in a row. Assuming that this attempts are independent, in what order he choses to take the tasks, in order to maximise his probability of passing the test.
12) A bomber wants to destroy a bridge. Two bombs are sufficient to destroy it. If four bombs are dropped, what is the probability that it is destroyed, if the chance of a bomb hitting the target is 0.4.
15) Anand plays with Karpov 3 games of chess. The probability that he wins a game is 0.5, losses with probability 0.3 and ties with probability 0.2. If he plays 3 games then find the probability that he wins atleast two games.
1q 18 5C3.1.6! + 2C1.4C1.1.6!/2! + 2C1.4C1.1.2C1.6!/2!2!
+ 5C3.1.2C1.6!2! +2 + 2C1.6!/3!2! + 2C1.4C1.6!/2!3! +6!/3! + 5C3 6!/3!
1in q 16 do u mean how many words with two vowels and two consonants can be made????
1q 17
6!/2!2!2! - 3C1( 5!/2!2!) +3C2(4!/2!) - 3!
there are three sets
kk, uu, tt
number of words without any restriction = 6!/2!2!2!
number of words where one set is together= 3C1(5!/2!2!)
no words where two sets are together=3C2(4!2!)
where all three together=3!
then we apply inclusion and exclusion
418 ) Find the no . of words each consisting of 3 consonants & 3 vowels that can be formed
from the letters of the word CIRCUMFERENCE.In how many of these 'c's will be together.
26.)In how many other ways can the letters of the word MULTIPLE be arranged;
(i) without changing the order of the vowels
(ii) keeping the position of each vowel fixed &
(iii) without changing the relative order of vowels & consonants
30 ) A man has 3 friends.In how many ways can he invite one friend everyday for dinner on 6 successive nights so that no friend is invited more than 3 times?
4SOME MORE....
16 ) How many arrangements of 2 vowels & 2 consonants can be made from the letters of the word " DEVASTATION " ?
17 ) fIND THE NO. OF WAYS IN WHICH THE LETTERS OF THE WORD " KUTKUT " can be arranged so that no two alike letters r together?
1prob 15
for station 1 next to cambridge there are 9 possible destinations
for station 2 there are 8 possible destinations
and so on
notice each of it is a different ticket
so total no of different tickets =9+8+7+.........+2+1
=45
we select 6 tickets
so possible ways = 45C6
1prob 3
let there be x men
now a woman will play 2 match with each man
so number of matches played by a woman are 2x
so total number of man-woman matches=2(2x)=4x
each man will play with x-1 man
so n.o. of man-man matches=x(x-1)
note that as each plays two matches with other we neednot check for repetitions
so from the given conditions
4x+66=x(x-1)
solving we get x=11
4@rickde : ALL ur ans r correct Can u give explnations for 3 & 15 th probs??
45) No. of ways in which 5 boys n 2 grps of girls are arranged = 7!
No. of ways in which both the grps of girls sit together = 6!
Required no. of ways = 7! - 6!