In a shop there are five types of ice-creams available. A child buys six ice-creams. Statement-1: Th

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 ${ }^{10} C_{5}$. 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.

Professor PC Thomas Classes · Answer

(b): 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 $4 B$ 's in a row $=\frac{10}{6 	imes \underline{4}}={ }^{10} C_{4}=$ Number of different ways the child can buy the six ice-creams.\ $	herefore \quad$ Statement-2 is true.\ So, Statement-1 is false, Statement-2 is true.\