Find the derivative of `y = 6^(2x)`.

Answer

C

Explanation

Let in 8 coupons S, U, R, F appears `x_(1), x_(2), x_(3), x_(4)` times. Then `x_(1) + x_(2) + x_(3) + x_(4) = 8`, where `x_(1), x_(2), x_(3), x_(4) ge 0`.
We have to find non-negative integral solution of the equation. The total number of such solution is
`.^(8+4-1)C_(4-1) = .^(11)C_(3) = 165`.
If a person gets at least one free packet, then he must get each coupon at least once, which is equal to number of positive integral solutions of the equation. The number of such solution is `.^(8-1)C_(4-1) = .^(7)C_(3) = 35`. Then, the porbability that he gets exactly one free packet is
`(35 - 1)//165 = 34//165`
The probability that he gets two free packets is `1.^(11)C_(3)=1//165`.