Five different games are to be distributed among 4 children randomly. The probability that each child get at least one game is `1//4` b. `15//64` c. `5//9` d. `7//12`

Answer

D

Explanation

Total ways of distribution = `n(S) = 4^(5)`
Total ways of distribution so that each child get at least one game
`n(E) = 4^(5) - .^(4)C_(1) 3^(5) + .^(4)C_(2) 2^(5) - .^(4)C_(3)`
`=1024 - 4 xx 243 + 6 xx 32 - 4 = 240`
Required probability `p = (n(E))/(n(S)) = (240)/(4^(5)) = (15)/(64)`