There are 4 notes of Rs. 100 and 5 other note | vedclass

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(C) Step $1$: Distribute the $4$ notes of Rs. $100$ among $3$ children such that each child gets at least one note. This is equivalent to finding the

Vedclass · Accepted Answer

$3^6$

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(C) Step $1$: Distribute the $4$ notes of Rs. $100$ among $3$ children such that each child gets at least one note. This is equivalent to finding the number of positive integer solutions to $x_1 + x_2 + x_3 = 4$,where $x_i \ge 1$. Using the stars and bars formula,the number of ways is $\binom{4-1}{3-1} = \binom{3}{2} = 3$ ways.Step $2$: Distribute the $5$ other distinct notes among $3$ children. Each of the $5$ notes can be given to any of the $3$ children in $3$ ways. Thus,the total ways for these $5$ notes is $3^5$.Step $3$: The total number of ways of distribution is the product of the ways from Step $1$ and Step $2$,which is $3 	imes 3^5 = 3^6$.

There are $4$ notes of Rs. $100$ and $5$ other notes of denominations Rs. $1$,Rs. $2$,Rs. $5$,Rs. $20$,and Rs. $50$. These $9$ notes are to be distributed among $3$ children such that each child receives at least one note of Rs. $100$. Find the total number of ways of distribution.

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