A box contains two white balls,three black ba | vedclass

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

Question

(A) The total number of balls in the box is $2 + 3 + 4 = 9$ balls.We need to select $3$ balls such that at least one black ball is included.The number

Vedclass · Accepted Answer

$64$

Vedclass · Answer

(A) The total number of balls in the box is $2 + 3 + 4 = 9$ balls.We need to select $3$ balls such that at least one black ball is included.The number of black balls is $3$ and the number of non-black balls is $2 + 4 = 6$.The selection can be made in the following $3$ mutually exclusive ways:$(i)$ $1$ black ball and $2$ non-black balls: $^3C_1 	imes ^6C_2 = 3 	imes 15 = 45$$(ii)$ $2$ black balls and $1$ non-black ball: $^3C_2 	imes ^6C_1 = 3 	imes 6 = 18$$(iii)$ $3$ black balls and $0$ non-black balls: $^3C_3 = 1$Therefore,the total number of ways = $45 + 18 + 1 = 64$.

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

Similar Questions

The number of ways of dividing $52$ cards amongst four players so that three players have $17$ cards each and the fourth player has just one card,is

How many $3$-letter words can be formed from the letters of the word '$EXPERTISE$',if repetition of letters is not allowed?

There are $6$ Men and $8$ Women in a club in which a committee of $5$ people has to be made. What will be the number of ways to select $5$ people if at most one man is selected?

Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated is

$A$ car can hold $2$ people in the front seat and $1$ person in the rear seat. If among $6$ persons $2$ can drive,then the number of ways in which the car can be filled is

Vedclass Test Series

Exam Paper Generator

Online Exam Module