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

(A) The total number of balls in the box is $2 + 3 + 4 = 9$.We need to select $3$ balls such that at least one is black.This can be calculated by subt

Vedclass · Accepted Answer

$64$

Vedclass · Answer

(A) The total number of balls in the box is $2 + 3 + 4 = 9$.We need to select $3$ balls such that at least one is black.This can be calculated by subtracting the number of ways to select $3$ balls with no black balls from the total number of ways to select $3$ balls.Total ways to select $3$ balls from $9$ is $^{9}C_{3} = \frac{9 	imes 8 	imes 7}{3 	imes 2 	imes 1} = 84$.Number of ways to select $3$ balls such that no black ball is chosen (i.e.,selecting from the $2$ white and $4$ red balls,total $6$ non-black balls) is $^{6}C_{3} = \frac{6 	imes 5 	imes 4}{3 	imes 2 	imes 1} = 20$.Therefore,the number of ways to select at least one black ball is $84 - 20 = 64$.

$A$ 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

$A$ student is to answer $10$ out of $13$ questions in an examination such that he must choose at least $4$ from the first $5$ questions. The number of choices available to him is

$A$ bag contains $5$ black and $6$ red balls. Determine the number of ways in which $2$ black and $3$ red balls can be selected.

The number of ways five alphabets can be chosen from the alphabets of the word $MATHEMATICS$,where the chosen alphabets are not necessarily distinct,is equal to :

Let the number of elements in sets $A$ and $B$ be $5$ and $2$ respectively. Then the number of subsets of $A \times B$ each having at least $3$ and at most $6$ elements is:

There are $25$ candidates for $12$ positions,out of which $5$ are from the reserved category. If $3$ positions are reserved and the remaining are open,in how many ways can the selection be made?

Vedclass Test Series

Exam Paper Generator

Online Exam Module