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)

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Solution

Q.
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 ______ [2026]

Ans.
(260)

$For n (s) = {}^{10}C_{4} = 210$

$(5, 4, 1, 1, 1), (5, 2, 2, 1, 1)$

$For n (p) = \frac{5!}{3!} + \frac{5!}{2! 2!} = 50$

$n (s) + n (p) = 210 + 50 = 260$

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