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) ⁸C₅ x ¹⁰C₄ (b) ¹⁰C₅ x ⁸C₄
(c) ¹⁸C₉ (d) none of these

Answer 1

Answer:

b

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Answer 2

The number of ways to draw 5 red and 4 white balls is $10C5\times 8C4$ ways and option (b) is correct.

Step-by-step explanation:

Given:

5 red and 4 white balls can be drawn from a bag containing 10 red and 8 white balls.

To Find:

The number of ways 5 red and 4 white balls can be drawn.

Formula Used:

if n number of quantities are given then r number of quantities can be drawn in $nCr$ ways.

The Fundamental principle of multiplication is that if there are p ways of doing one thing and q ways of doing another thing, then there are p× q ways of performing both actions.

Solution:

As given- 5 red and 4 white balls can be drawn from a bag that contains 10 red and 8 white balls.

A Bag contains 10 red balls and 8 white balls, so from the 10 red balls 5 red balls can be drawn $=10C5$ ways

Similarly from 8 white balls, 4 balls can be drawn $=8C4$   ways.

By the fundamental principle of multiplication  5, red, and 4 white balls can be drawn $=10C5\times 8C4$ ways.

Thus, the number of ways to draw  5 red and 4 white balls are $10C5\times 8C4$ ways, and option (b) is correct.