Question
Download Solution PDFConsider the digits 3, 5, 7, 9. What is the number of 5-digit numbers formed by these digits in which each of these four digits appears?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula used:
n! = n × (n - 1) × (n - 2) × ..... × 3 × 2 × 1
5! = 5 × 4 × 3 × 2 × 1 = 120
2! = 2 × 1 = 2
Calculation:
Four cases can possible: (3, 5, 7, 9, 3), (3, 5, 7, 9, 5), (3, 5, 7, 9, 7), (3, 5, 7, 9, 9)
For (3, 5, 7, 9, 3)
Number of arrangements = \(\rm \frac{5!}{2!}\)
⇒ \(\rm \frac{120}{2}\)
⇒ 60
Similarly for all 4 cases 60 ways
⇒ 60 × 4
⇒ 240
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