Question

A bag contains 10 toys out of which 3 are rectangular and rest are spherical. ankit was asked to draw a random sample of 6 toys from the bag. the sample can have atmost 2 rectangular toys and it must not contain all the toys of same shape. how many such samples can be drawn by ankit? * 172 * 168 * 166 * 188 * none of these

Answer 1

168 is your answer bhi

Answer 2

Answer:  The correct option is (B) 168.

Step-by-step explanation:  Given that a bag contains 10 toys out of which 3 are rectangular and rest are spherical. Ankit was asked to draw a random sample of 6 toys from the bag.

The sample can have at most 2 rectangular toys and it must not contain all the toys of same shape.

We are to find the number of such samples that can be drawn by Ankit.

According to the given information, the sample can have following combinations :

1 rectangular toy, 5 spherical toys

and

2 rectangular toys, 4 spherical toys.

Since there are 3 rectangular shaped toys, so the number of spherical shaped toys = 10 - 3 =7.

So, if A denote the collection of all the samples drawn by Ankit, then we have

$n(A)\\\\=^3C_1\times ^7C_5+^3C_2\times ^7C_4\\\\\\=\dfrac{3!}{1!(3-1)!}\times \dfrac{7!}{5!(7-5)!}+\dfrac{3!}{2!(3-2)!}\times \dfrac{7!}{4!(7-4)!}\\\\\\=\dfrac{3\times2!}{1\times2!}\times\dfrac{7\times6\times5!}{5!\times2\times1}+\dfrac{3\times2!}{1\times2!}\times\dfrac{7\times6\times5\times4!}{4!\times3\times2\times1}\\\\\\=3\times21+3\times35\\\\=63+105\\\\=168.$

Thus, the required number of samples drawn by Ankit is 168.

Option (B) is CORRECT.