Question:
The number of positive integral solution of $abc = 30$ is
The number of positive integral solution of $abc = 30$ is
Updated On: Jun 18, 2022
- 30
- 27
- 8
- None of these
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The Correct Option is B
Solution and Explanation
We have : $30 = 2 \times 3 \times 5$.
So, $2$ can be assigned to either $a$ or $b$ or $c$
i.e. $2$ can be assigned in $3$ ways.
Similarly, each of $3$ and $5$ can be assigned in $3$ ways.
Thus, the number of solutions is $3 \times 3 \times 3 = 27$.
So, $2$ can be assigned to either $a$ or $b$ or $c$
i.e. $2$ can be assigned in $3$ ways.
Similarly, each of $3$ and $5$ can be assigned in $3$ ways.
Thus, the number of solutions is $3 \times 3 \times 3 = 27$.
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Concepts Used:
Permutations
A permutation is an arrangement of multiple objects in a particular order taken a few or all at a time. The formula for permutation is as follows:
\(^nP_r = \frac{n!}{(n-r)!}\)
nPr = permutation
n = total number of objects
r = number of objects selected
Types of Permutation
- Permutation of n different things where repeating is not allowed
- Permutation of n different things where repeating is allowed
- Permutation of similar kinds or duplicate objects