The number of ways in which 35 apples can be | vedclass

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(B) This is a problem of distributing $n$ identical items into $r$ distinct groups where each group can receive zero or more items.The formula for thi

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$666$

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(B) This is a problem of distributing $n$ identical items into $r$ distinct groups where each group can receive zero or more items.The formula for this is given by the stars and bars theorem: $\binom{n+r-1}{r-1}$.Here,$n = 35$ (number of apples) and $r = 3$ (number of boys).Substituting the values: $\binom{35+3-1}{3-1} = \binom{37}{2}$.Calculating the value: $\binom{37}{2} = \frac{37 	imes 36}{2 	imes 1} = 37 	imes 18 = 666$.Thus,the number of ways is $666$.

The number of ways in which $35$ apples can be distributed among $3$ boys so that each can have any number of apples,is

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