Question

A box contains 3 white balls, 4 black balls and 5 yellow balls. in how many ways can 4 balls be drawn from the box, if at least one yellow ball is to be included in the draw?

Answer 1

no. of ways = 27

to drawn 4 ball from box if at least one yellow ball is to be included

Answer 2

There are 460 ways to draw at least one yellow ball from the box.

Given,

A box contains 3 white balls, 4 black balls, and 5 yellow balls.

To Find,

The number of ways at least one yellow ball is included in the draw.

Solution,

A box contains,

White balls = 3

Black balls = 4

Yellow balls = 5

So,

Let's solve the question using the given information,

⇒ Number of ways choosing 1 yellow ball and 3 other different balls = ⁵C₁×⁷C₃ = 5×35 = 175.

⇒Number of ways choosing 2 yellow balls and 2 other different balls = ⁵C₂×⁷C₂ = 10×21 =210.

⇒Number of ways choosing 3 yellow balls and 1 other different ball = ⁵C₃×⁷C₂ = 10 ×7 = 70.

⇒Number of ways choosing 4 yellow balls = ⁵C₄ = 5.

So, total number of required ways = 175+210+70+5 = 460.

There are 460 ways to draw at least one yellow ball from the box.

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