Question

In how many ways can $5$ red and $4$ white balls be drawn from a bag containing $10$ red and $8$ white balls?

• A. ${}^{8}c_5\times {}^{10}c_4$
• B. ${}^{8}c_4\times {}^{10}c_5$
• C. ${}^{18}c_9$
• D. $Noneofthese$

Answer 1

The correct option is B

${}^{8}c_4\times {}^{10}c_5$

Explanation for the correct option:

Step 1. Formula for Combination= ${}^{\mathbf{n}}\mathit{c}_{\mathbf{r}}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{n}\mathbf{!}}{\mathbf{r}\mathbf{!}\mathbf{(}\mathbf{n}\mathbf{-}\mathbf{r}\mathbf{)}\mathbf{!}}$

Step 2. Number of ways can be drawn.

We have 10 red balls and 8 white balls. out which 5 red and 4 white balls can be drawn

Number of ways = ${}^{8}c_4\times {}^{10}c_5$

Hence correct option is $\left(B\right)$.