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In a shop there are five types of ice-creams (each type is available unlimited).A child buys six ice-creams.
Statement-1: The number of different ways the child can buy the six ice-creams is $^{10} C_{5}$ .
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.

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Statement - 1 is true, Statement - 2 is true, Statement - 2 is a correct explanation for Statement - 1.

Statement - 1 is true, Statement - 2 is true; Statement - 2 is not a correct explanation for Statement - 1.

Statement -1 is true, Statement - 2 is false.

Statement - 1 is false, Statement - 2 is true.

answer is C.

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Detailed Solution

We have to find the number of integral solutions if $x_{1} + x_{2} + x_{3} + x_{4} + x_{5} = 6$ and that equals $^{5 + 6 - 1} C_{5 - 1} =^{10} C_{4}$

Thus Statement-1 is false

Number of different ways of arranging 6A’s and 4B’s in a row $= \frac{10}{6 \times 4} =^{10} C_{4}$ = Number of different way the child can buy the six ice-creams

$∴$ Statement-2 is true

So, Statement-1 is false, Statement-2 is true.

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