Question
Let S denote the set of 4-digit numbers a b c d 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 \_\_\_\_
JEE Main
Mathematics
Permutation Combination
2026
JEE Main 2026 (23 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. A
- B. B
- C. C
- D. D
Answer
A. A
Step-by-step solution
n(S): Choose 4 distinct digits from \ 0,1, ,9\ and arrange in decreasing order. n(S) = 10 4 = 210. n(P): 5-digit numbers with digit product = 20 = 2^2 5. All digits 1 (else product = 0). Must include exactly one 5, remaining 4 digits multiply to 4. Case 1: \ 1,1,1,4,5\ : 5! 3! = 20 arrangements. Case 2: \ 1,1,2,2,5\ : 5! 2! 2! = 30 arrangements. n(P) = 50. Hence n(S) + n(P) = 210 + 50 = 260.
Related: Mathematics — Permutation Combination · All PYQ Banks