NIMCET 2016 — Mathematics PYQ

Concept:
- The number of ways for selecting r from a group of n (n > r) = "C_r
- The probability of particular case = $\frac{\text{Number of ways for the case can be executed}}{\text{Total number of ways for selection}}$

Calculation:
The total number of caps = 2 + 4 + 5 + 1 = 12
The number of ways for selecting four caps = 12C_4
The total number of caps other than green = 12 - 5 = 7

The number of ways for selecting four caps other than green = 7C_4

The probability of selecting four caps and none of them are green P(A') = $\frac{\text{The number of ways for selecting four caps other than green}}{\text{The number of ways for selecting four caps}}$

$\Rightarrow$ P(A') = $\frac{7C_4}{12C_4}$

$\Rightarrow$ P(A') = $\frac{7!}{4!(12-4)!}$

$\Rightarrow$ P(A') = $\frac{7}{99}$