1yes I agree with u, that is why answer given is right, and method is the first one
5 ladies and 5 gents are to be arranged in a row..Find no. of ways so that no two ladies are together
Method 1
place 5 gents on 5 seats(leaving one space) with 5! ways and then we have 6! ways to place ladies in vacant seats
ans=6!.5!
Method 2
Total ways to arrange 10 people =10!
Taking all ladies together ,no. of ways=5!.6!
so ans is 10!-(6!.5!)
which method is correct ????????
and ya ...ans is 6!.5!....but atleast tell me my mitskae plzzz
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19 Answers
112nd method is wrong .
in 2nd method you have to subtract cases of 2,3 & 4 ladies together.
106@uttara.. method 1 is definitely correct..
Q2. can u illustrate the mistake in My solution..
I cant seem to find it.. (perhaps due to boards tension..)
4Ya Even I made the same mistake as eureka
Ya u people r correct
So ans is 1st method
4Asish u made a calc mistake
Ans is coming out to be 8
Check ur last step !!
106For Q1. second method is wrong.
reason is madhu's post given in #12
Q2. 24 = 23.31
Find exponentr of 2 and 3 in 25!
25! = 222.310I (I is integer) = 221.37.2.33*I
= 87*27*2*I
So, ans is 7
1the 2nd method is wrong because, it makes sure that 5 ladies arent together..but it does not make sure that 2,3,4 ladies arent together
1@ Uttara,
yeah method one also includes case L G G L G L G L G L....but this is not a contradiction, as it still satisfies the condition that no two ladies should be together....and so method 1 is right.
4NO Madhu eureka's Qs says that no 2 ladies r together
So the ladies r to be separated by 1 or 2 or ... gents such that they r never together
1in Q1, the 2nd method is wrong because it does not account for the cases in which less than 5 but more than 1 ladies are together.
24hmm....still wondering abt Q1 becoz both ways it seems right..
for Q2 i dont have ans...but if u r 100% confident with ur method ,,theni accept ur soln...otherwise we can wait for a someone else to chip in with some for facts
4@eureka :
Ya So I say that ans must have been 2
Wonder y its given the other way [7]
4This is not very logical but
25 ! ---> 2 x 12 ;
3 x 8 ;
4 x 6 ;
24 ;
3 x 4 x 2 (from 9 14 16) ;
3 x 4 x 2 (from 9 16 18 ) ;
3 x 4 x 2 (from 15 16 22) ;
SO 7 ??
24so whats the problem here ??
L G G L G L G L G L
no 2 ladies together condition is staisfied...
4Method wise 2 seems correct
Becz In Method 1 Apart from those alternating cases u may have one case this way too
L G G L G L G L G L