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

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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:

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