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 C5 10 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

x1+x2+x3+x4+x5=6No. of ways = 10C4Statement-1 is falseNumber of different ways of arranging 6 A’s and 4B’s in a row 10!6!4!=10C4= The number of different ways the child can buy the six ice creams

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 C5 10 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

x1+x2+x3+x4+x5=6No. of ways = 10C4Statement-1 is falseNumber of different ways of arranging 6 A’s and 4B’s in a row 10!6!4!=10C4= The number of different ways the child can buy the six ice creams

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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 ${}^{10}C_{5}$
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 false

Statement-1 is false, Statement-2 is true

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

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

answer is B.

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Detailed Solution

$x_{1} + x_{2} + x_{3} + x_{4} + x_{5} = 6$
No. of ways = $10_{C_{4}}$
Statement-1 is false
Number of different ways of arranging 6 A’s and 4B’s in a row $\frac{10!}{6! 4!} = 10_{C_{4}} =$ The number of different ways the child can buy the six ice creams