A box contains 2 white balls,3 black balls an | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Total number of balls $= 2 + 3 + 4 = 9$.Number of black balls $= 3$.Number of non-black balls $= 2 + 4 = 6$.We need to select $3$ balls such that

Vedclass · Accepted Answer

$64$

Vedclass · Answer

(C) Total number of balls $= 2 + 3 + 4 = 9$.Number of black balls $= 3$.Number of non-black balls $= 2 + 4 = 6$.We need to select $3$ balls such that at least one is black.This can be done in the following ways:$1$ black and $2$ non-black balls: ${}^{3}C_{1} 	imes {}^{6}C_{2} = 3 	imes 15 = 45$.$2$ black and $1$ non-black balls: ${}^{3}C_{2} 	imes {}^{6}C_{1} = 3 	imes 6 = 18$.$3$ black and $0$ non-black balls: ${}^{3}C_{3} 	imes {}^{6}C_{0} = 1 	imes 1 = 1$.Total ways $= 45 + 18 + 1 = 64$.

$A$ box contains $2$ white balls,$3$ black balls and $4$ red balls. In how many ways can $3$ balls be drawn from the box,if at least one black ball is to be included in the draw?

Similar Questions

In how many different ways can the letters of the word '$DETAIL$' be arranged in such a way that the vowels occupy only the odd positions?

$A$ father with $8$ children takes them $3$ at a time to the Zoological gardens,as often as he can without taking the same $3$ children together more than once. The number of times he will go to the garden is

Find $\sum_{r=1}^{5} C(5, r)$

How many $3$-digit even numbers can be formed using the digits $0, 2, 3, 5, 7$ when repetition is not allowed?

$A$ committee of $5$ members is to be formed out of $3$ trainees,$4$ professors,and $6$ research associates. In how many different ways can this be done if the committee must have $2$ trainees and $3$ research associates?

Vedclass Test Series

Exam Paper Generator

Online Exam Module