11324 ways
Rekha married Shivram and had 4 sons. Varsha married Ajoy and had 4 sons. Both the couples had divorce and after that Shivram married Varsha while Ajoy married Rekha. They too had 3 sons each from their wedlocks. How many selections of 8 children can be made from the 14 childrnen so that each of them have equal number of sons in the selection.?
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11 Answers
11Solution
Consider 4 Groups 1) RS 2)VA 3)AR 4)VS
Sons 4 4 3 3
Therefore 2 from each.
Therefore total ways = 4C2 * 4C2 * 3C2 * 3C2
= 2* 3 *2*3*3*3
6*6*9
= 36 *9
= 324
62basically this boils down to chosing equal no from 4,4,3,3 (why?)
this is equal to
4x4x3x3 + 6x6x3x3 + 4x4
= 160+324 = 484
62why cant they all have a casewhere they chose 1 child from each couple or 3 children from each couple?
11No man i made the same mistake.
I took Combination instead of Permutation
Bhaiyya any tips for selection of P or C
1@Nishant Bhaiya
bhaiya ... can u plz explain what have u done??
62I did this in this way...
a bit long but see if it helps
let "a" kids from 1st couple, "b" from 2nd, "c" from 3rd and "d" from 4th.
hence
rekha has a+d kids
shivam has a+c kids
equate, d=c
similarly you get a=b=c=d
now i took cases when these are 1 or 2 or 3
and added for these 3 cases.