Seven sportsmen (named A,B,C,D,E,F and G) buy 7 hats choosing randomly out of 4 available
colors (say G,R,W and Y).
What is the probability that all
the colors were chosen?
Total Number of ways in which caps can be selected
= 4^7 (A can select 4 ways, B can select 4 ways , ....)
Let G,R,W,Y are already selected, the other caps can be selected as
1) 3 of different colors
2) 2 of same color, 1 of other color
3) 3 of the same color
Case 1)
No. of ways 3 colors can be selected = 4C3 = 4
No. of ways they can be selected by 7 players = 7!*4/(2!*2!*2!) = 2520
Case 2)
No. of ways 2 same 1 different can be selected = 4C2 = 6
No. of ways they can be selected by 7 players = 12*7!/(3!*2!) = 5040
Case 3)
No. of ways 3 same can be selected = 4
No. of ways they can be selected by 7 players = 4*7!/4! = 840
Total No. of ways = 8400
=> Probability = 8400/16384 = 0.5126953125
Edited on May 10, 2010, 9:35 am

Posted by Praneeth
on 20100510 09:19:54 