Question

In the 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 6As and 4Bs in a row

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

Answer 1

Answer: (C)

Statement-1 is false, Statement-2 is true

Let $x_k$ denotes the types of ice-creams available.
$x_1+x_2+x_3+x_4+x_5=6$
$x_k\ge 0$
No. of ways the child can buy six ice-creams ${=}^{6+5-1}{C}_{5-1}={10}_{C_4}=\frac{10!}{6!.4!}$
Hence, statement 1 is false.
Number of ways of arranging 6A's and 4B's in a row $=\frac{10!}{6!.4!}$
Hence, statement 2 is true.