In how many ways can 10 balls be divided betw | vedclass

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(C) Let the two boys be $A$ and $B$.Case $1$: Boy $A$ receives $2$ balls and boy $B$ receives $8$ balls. The number of ways to choose $2$ balls out of

Vedclass · Accepted Answer

$90$

Vedclass · Answer

(C) Let the two boys be $A$ and $B$.Case $1$: Boy $A$ receives $2$ balls and boy $B$ receives $8$ balls. The number of ways to choose $2$ balls out of $10$ for boy $A$ is given by $\binom{10}{2} = \frac{10!}{2!8!} = \frac{10 	imes 9}{2 	imes 1} = 45$.Case $2$: Boy $A$ receives $8$ balls and boy $B$ receives $2$ balls. The number of ways to choose $8$ balls out of $10$ for boy $A$ is given by $\binom{10}{8} = \frac{10!}{8!2!} = 45$.Since these are two distinct scenarios,the total number of ways is $45 + 45 = 90$.

In how many ways can $10$ balls be divided between two boys,if one receives two balls and the other receives eight balls?

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