Q56 / 105 · JEE Main 2008 · Mathematics
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 ${ }^{10} \mathrm{C}_5$.
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 $6 \mathrm{~A}^{\text {'s }}$ and 4 B's in a row.
- Correct answerAStatement $-1$ is false, Statement $-2$ is true
- BStatement $-1$ is true, Statement $-2$ is true, Statement $-2$ is a correct explanation for Statement $-1$
- CStatement $-1$ is true, Statement $-2$ is true; Statement $-2$ is not a correct explanation for Statement $-1$.
- DStatement $-1$ is true, Statement $-2$ is false.
Solution
$$
\begin{aligned}
& x_1+x_2+x_3+x_4+x_5=6 \\
& 5+6-1 C_{5-1}={ }^{10} C_4
\end{aligned}
$$
Hence, the correct answer is option: 'A'.