help me in maths...:)

CPT 6048 views 4 replies

1).The number of ways in which 12 students can be equally divided into three groups ?(combination chapter question and the answer is 5775 is given)

2).A committee of 3 ladies and 4 gents is to be formed out of 8 ladies and 7 gents.Mrs.x refuses to serve in a committee in which Mr.y is a member.The number of such committee is ?(combination chapter answer is 1540 is given )

3).The supreme court has given a 6 to 3 decision upholding a lower court;the number of ways it can give a majority decision reversing the lower court is ?(combination chapter answer is given 256 )

4).The total number of ways in which six 't' and four '-'signs can be arranged in a line such that no two '-'signs occur together is ?(permutation chapter answer is given 35 in book )

help me if u know the solution :)

Replies (4)

All possible committees without any restriction are    8C3   x  7C4   =   1960

Committees when Mrs. X & Mr. Y are together are      7C2   x   6C3   =     420

So, committees when they are never together are  1960  -  420  =  1540

Majority decision against the lower court is possible in the following cases :

5 judges against the decision & 4 in favour   =   9C5   x   4C4   =   126

6 judges against the decision & 3 in favour   =   9C6   x   3C3   =     84

7 judges against the decision & 2 in favour   =   9C7   x   2C2   =     36

8 judges against the decision & 1 in favour   =   9C8   x   1C1   =       9

9 judges against the decision & 0 in favour   =   9C9   x   0C0   =       1

Total ways possible is the sum of all these                                       256

Let us place the 6 t's first. Since all the t's are identical there is no question of arranging them. Since no two '-' signs must be together there are 7 places to be selected to place the 4 t ' - ' signs. Since all the ' - ' signs are identical there is no question of arranging them.

Hence we need to select 4 out of 7 places. This can be done in 7C4 ways  =  35 ways

12 students are to be divided into 3 equal groups of 4 each.

This can be done in     12!  /  (3!  x  4!  x  4!  x  4!)      ways


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