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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 ${ }^{10} \mathrm{C}_5$.
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.
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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.
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Verified Answer
The correct answer is:
Statement $-1$ is false, Statement $-2$ is true
Statement $-1$ is false, Statement $-2$ is true
$$
\begin{aligned}
& x_1+x_2+x_3+x_4+x_5=6 \\
& 5+6-1 C_{5-1}={ }^{10} C_4
\end{aligned}
$$
\begin{aligned}
& x_1+x_2+x_3+x_4+x_5=6 \\
& 5+6-1 C_{5-1}={ }^{10} C_4
\end{aligned}
$$
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