Quantitative Reasoning

Permutation & Combination

Medium

How many 5-digit numbers can be formed by using digits 1, 2, 3, 4, 5 if 2 and 3 cannot come together?

✅ Correct Option: 4

Total arrangements of the five digits $= 5! = 120$ .

Treating 2 and 3 as one block gives $4! \times 2! = 48$ arrangements in which they are together.

Required $= 120 - 48 = 72$ .

Note: The question does not state whether digits may repeat; we have taken each of the five digits to be used exactly once.

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Solution

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