The number of ways in which one or more balls | vedclass

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

Question

(D) To select one or more balls from $10$ white,$9$ green,and $7$ blue balls,we consider the choices for each color.For white balls,we can choose $0,

Vedclass · Accepted Answer

$879$

Vedclass · Answer

(D) To select one or more balls from $10$ white,$9$ green,and $7$ blue balls,we consider the choices for each color.For white balls,we can choose $0, 1, 2, \dots, 10$ balls,which gives $(10 + 1) = 11$ options.For green balls,we can choose $0, 1, 2, \dots, 9$ balls,which gives $(9 + 1) = 10$ options.For blue balls,we can choose $0, 1, 2, \dots, 7$ balls,which gives $(7 + 1) = 8$ options.The total number of combinations including the case where no balls are selected is $11 	imes 10 	imes 8 = 880$.Since we must select one or more balls,we subtract the case where zero balls are selected (the case where we choose $0$ white,$0$ green,and $0$ blue).Therefore,the required number of ways $= 880 - 1 = 879$.

The number of ways in which one or more balls can be selected out of $10$ white,$9$ green,and $7$ blue balls are:

Similar Questions

In a group of $6$ boys and $4$ girls,four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?

In how many different ways can the letters of the word $ALGEBRA$ be arranged in a row if:
$(I)$ The $2$ $A$s are together?
$(II)$ The $2$ $A$s are not together?

There are $16$ points in a plane, out of which $6$ are collinear. How many lines can be drawn by joining these points?

The number of positive integral solutions of the equation $xyz = 3000$ is:

We wish to select $6$ persons from $8,$ but if the person $A$ is chosen,then $B$ must be chosen too. In how many ways can the selection be made?

Vedclass Test Series

Exam Paper Generator

Online Exam Module