Multiple choice

In how many different ways can the numbers 3576124 be arranged using each digit only once in each arrangement such that the digits 6 and 7 are at the extreme ends in each arrangement?

  1. 120

  2. 240

  3. 720

  4. 5040

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Digits 6 and 7 must be at extreme ends, with 2! arrangements (6 at left, 7 at right OR 7 at left, 6 at right). Remaining 5 digits (3, 5, 7, 1, 2, 4 but wait, 7 is used at ends, so remaining are 3, 5, 1, 2, 4) can be arranged in middle 5 positions in 5! = 120 ways. Total = 2! × 5! = 2 × 120 = 240. This matches option B.

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