Question

A box contains 3 red balls, 4 blue balls, and 5 yellow balls. in how many ways can 4 balls be drawn from the box if at least 1 yellow ball is to be included in the draw? 652 356 547 425

Answer 1

Answer:

3 ways

Step-by-step explanation:

I hopeit will help you

Answer 2

The required number of ways is 425 and option (d) is correct.

Step-by-step explanation:

Given:

3 red balls, 4 blue balls, and 5 yellow balls are contained in a box.

4 balls are drawn from the box if at least 1 yellow ball is to be included in the draw.

To Find:

The required number of ways.

Solution:

As given- 3 red balls, 4 blue balls, and 5 yellow balls are contained in a box.

As given - 4 balls are drawn from the box if at least 1 yellow ball is to be included in the draw.

Considering 4 balls drawn ( 1 yellow and 3 others)

Number of ways  to draw 1 yellow and 3 others $=4C1 \times 8C3$  

Considering 4 balls drawn ( 2 yellow and 2 others)

Number of ways  to draw 2 yellow and 2 others  $=4C2 \times 8C2$

Considering 4 balls drawn ( 3 yellow and 1 other)

Number of ways  to draw 3 yellow and 1 others  $=4C3 \times 8C1$

Considering 4 balls drawn ( 4 yellow)

Number of ways to draw 4 yellow   $=4C4$

Therefore, the required number of ways  $=4C1 \times 8C3+4C2 \times 8C2+4C3 \times 8C1 +4C4$

$= \frac{4!}{(4-1)!\ 1!} \times \frac{8!}{(8-3)!\ 3!} +\frac{4!}{(4-2)!\ 2!}\times\frac{8!}{(8-2)!\ 2!} +\frac{4!}{(4-3)!\ 3!} \times \frac{8!}{(8-1)!\ 1!} +\frac{4!}{(4-4)!\ 4!}$

$= \frac{4!}{3!\ 1!} \times \frac{8!}{5!\ 3!} +\frac{4!}{ 2!\ 2!}\times\frac{8!}{ 6!\ 2!} +\frac{4!}{ 1!\ 3!} \times \frac{8!}{ 7!\ 1!} +\frac{4!}{ 0!\ 4!}$

$= \frac{4. 3!}{3!\ 1!} \times \frac{8.7.6.5!}{5!\ 3!} +\frac{4.3.2!}{ 2!\ 2!}\times\frac{8.7.6!}{ 6!\ 2!} +\frac{4.3!}{ 1!\ 3!} \times \frac{8.7!}{ 7!\ 1!} +\frac{4!}{ 0!\ 4!}$

$= 4\times 56+ 6 \times 28 + 4\times 8+ 1$

$= 224+168+ 32+1$

$= 425$

Thus, the required number of ways is 425, and option (d) is correct.

Correct Question

A Box contains 3 red balls, 4 blue balls, and 5 yellow balls. In how many ways  4 balls can be drawn from the box if at least 1 yellow ball is to be included in the draw?

Options:

(a). 652

(b). 356

( c). 547

(d). 425