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Question

# In a shop there are five types of ice creams available. A child buys six ice creams. Statement 1: 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 false, statement 2 is true.
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B
Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1.
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C
Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1.
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D
Statement 1 is true, statement 2 is false.
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Solution

## The correct option is A Statement 1 is false, statement 2 is true.In shop there are five different types of ice creams. Let a child buy xi ice creams of type i, where i = 1, 2, 3, 4, 5. Child buys six ice creams. ∴ x1+x2+x3+x4+x5=6 where 0≤xi≤6 So total number of ways in which child can buy ice creams = number of non-negative solutions of above equations = placing 6 identical balls in 5 different boxes = 6+5−1C5−1=10C4

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