11Sir, 2nd question ka answer is given as 600. These questions are from KC Sinha.
1)In how many ways can the letter of the word 'ARRANGE' be arranged so that
a)the 2 A's are together but not the 2 R's ?
b)neither the two A's nor the two R's are together?
2)How many numbers greater than 10000 can be formed from the digits of the numbers 112340?he numbers may be either of 5 digits or 6 digits.
Am getting the answer as 456, which is incorrect [2]
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9 Answers
62no of words in which A's are together
minus
no of words in which A's and R's are together..
= 6!/2 - 5! = 2. 5!
622)How many numbers greater than 10000 can be formed from the digits of the numbers 112340?he numbers may be either of 5 digits or 6 digits.
all that you should do is make a 6 digit number and allow 0 to be the first digit [1]
so the answer will be 6!/2! = 360
11
392)
2 cases :
cas1: no :of 5 digit numbers we can make
sub case1:
those with 1 as the left most digit
then remaining 4 places can be filled in 5P4 ways =120
sub case 2: those with 2,3,4 as left most digit
so left most can be filled in 3 ways and remaining 4 places can be filled in 5P4/2! ways
so for sub case 2 , totla numbers =3x5P4/2!
so total no:of 5 digit numbers we can make = 120 +3x5P4/2! =300
case2: no of 6 digit numbers we can make
sub case 1: with 1 as left most digit
then remaining 5 digits can be filled in 5! ways = 120
sub case 2: with 2,3,4 as left most digit
then remaining 5 digits can be filled in 5!/2! ways
so total numbers =3x5!/2!=180
so total 6 digit numbers =300
so total numbers we can make>10,000 =300+300=600
39and nishant sir
with reference to your comment
all that you should do is make a 6 digit number and allow 0 to be the first digit
then in that case u only can calculate all 5 digit numbers >10000
u will be missing the 6 digit numbers
and coming to your calculation 6!/2! , that is permuattion of 6 things in 6 places when 2 are alike
that doesnt complement your above comment in anyway :P
62I did not say that you have to force 0 as the first digit..
what i tried to imply was that if 0 is teh first digit... nothting to worry.. it will give us a 5 digit number!
figured out my mistake..
i missed those 5 digit numbers where 0 is a part of the number..
39exactly that wat i was going to say
while doing 6!/2! u missed those 5 digit numbers of which 0 is a part
11Thanks Nishant Sir and id no 711.(kitne naam change karte ho aap [3])
111)In an election the number of candidates is one more than the number of members to be elected. If a voter can vote in 30 different ways, find the number of candidates.(A voter has to vote for at least one candidate)
2)In a plane there are n lines, no two of which are parallel and no three are concurrent. How many triangles can be formed with their points of intersection as vertices?(Please dont make use of binomial theorem while solving this one, because I wanna know the method by which this kinda sums can be solved using PnC concepts only)
3)There is a convex polygon of n sides (n>5). Triangles are formed by joining the vertices of the polygon,how many triangles are there and how many of them have no side side common with any of the sides of the polygon.