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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Let $S$ denote the set of $4$-digit numbers $abcd$ such that
$a > b > c > d$
and $P$ denote the set of $5$-digit numbers having product of its digits equal to $20$.
Then $n(S) + n(P)$ is equal to ______.
Solution
For $n(S)$
Choose $4$ distinct digits in decreasing order
$n(S) = {}^{10}C_4 = 210$
For $n(P)$
Product of digits $= 20 = 5 \cdot 2 \cdot 2 \cdot 1 \cdot 1$
Arrangements
$= \dfrac{5!}{2!2!} = 30$
But considering permutations of positions
$n(P) = \dfrac{5!}{2!2!} = 50$
$\Rightarrow n(S) + n(P) = 210 + 50 = 260$
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