A team of 8 couples (husband and wife) attend a lucky draw in which 4 persons picked for a prize. Then the probability that there is at least one couple is

Options

A. `11//39`
B. `12//39`
C. `14//39`
D. `15//39`

Answer

D

Explanation

We have,
Probability of selecting at least one couple for the prize
`=1-` Probability of not selecting any couple for the prize
`=1-((.^(16)C_(1)xx .^(14)C_(1)xx .^(12)C_(1)xx .^(10)C_(1)4!))/(.^(16)C_(4))`
`=1-(16xx14xx12xx10)/(16xx15xx14xx13)=(15)/(39)`.