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Question

In a shop there are five types of ice-creams available. A child buys six ice-creams.
Statement-l: The number of different ways the child can buy the six ice-creams is 10C5.
Statement-2: The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A's and 4 B's in a row.

A
Statement-1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1.
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B
Statement-1 is true, Statement-2 is false.
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C
Statement-1 is false, Statement-2 is true.
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D
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
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Solution

The correct option is D Statement-1 is false, Statement-2 is true.
Statement-l: Number of ways = Number of non negative integral solutions of the equation T1+T2+T3+T4+T5=6
=6+51C51=10C4
Statement-l is wrong.
Statement-2:
Number of different ways of arranging 6A's and 4B's in a row =10!6!4!=10C4
Statement-2 is correct.

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