Discussion

Explanation:

Let us label the 5 digits in the number i.e., 5 4 3 2 1.

We need to place 1 digit between 3 and 7.

Hence, we can place 3 and 7 at the following positions:

5 and 3, 4 and 2 or 2 and 1 i.e., 3 ways.

For each of these 3 places, 3 and 7 can be arranged in 2 ways, hence total number of ways of arranging 3 and 7 = 3 × 2 = 6 ways.

Now, for each of these 6 ways, rest 3 digits can be arranged in 3! = 6 ways.

Hence, total number of 5-digit numbers that can be formed having exactly 1 digit between 3 & 7 = 6 × 6 = 36 ways.

Hence, 36.

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