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Fundamental Principle of Counting

Note of Rs. 1...

Question

$4$ note of Rs. $100$ and $5$ notes in which first of Rs. $1$ , second of Rs. $2$ , Third of Rs. $5$ , fourth of Rs $20$ and fifth one of Rs $50$ distributed among $3$ children such that each child receives at least one note of Rs. $100$ . The total number of ways of distribution

$3 \times 5^{3}$

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$5^{3} \times 3$

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$3^{6}$

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None of these

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Solution

The correct option is C
$3^{6}$

Explanation for the correct option:
Step 1: Find the number of ways to distribute Rs. $100$ notes.
Given: $4$ notes of Rs. $100$ and $3$ children.
Since notes are identical. So, it can be given in only one way to distribute Rs. $100$ notes.
Step 2: Find the number of ways to distribute the remaining notes.
Given: $5$ notes consisting of Rs $1, 2, 5, 20$ and $50$
Also, one Rs $100$ is left.
So, number of ways in which $6$ notes can be distributed in any manner among $3$ people $= 3^{6}$
Hence, option (C) is the correct answer.

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