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 ${}^{10}{C}_5$.
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.

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

Answer 1

Answer: (C)

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

Statement-l: Number of ways $=$ Number of non negative integral solutions of the equation $T_1+T_2+T_3+T_4+T_5=6$
${=}^{6+5-1}{C}_{5-1}{=}^{10}{C}_4$
$\therefore$ Statement-l is wrong.
Statement-2:
Number of different ways of arranging $6A$'s and $4B$'s in a row $=\frac{10!}{6!4!}{=}^{10}{C}_4$
$\therefore$ Statement-2 is correct.