In how many different ways can the numbers '256974 be arranged, using each…
2023
In how many different ways can the numbers '256974 be arranged, using each digit only once in each arrangement, such that the digits 6 and 5 are at the extreme ends in each arrangement?
- A.
48
- B.
720
- C.
36
- D.
360
Attempted by 21 students.
Show answer & explanation
Correct answer: A
Answer: 48
Reason:
Place the digits 6 and 5 at the two extreme ends. They can be arranged in 2! = 2 ways (6 at left and 5 at right, or 5 at left and 6 at right).
Arrange the remaining four distinct digits (2, 9, 7, 4) in the middle four positions. That gives 4! = 24 ways.
Multiply the counts: total arrangements = 2! × 4! = 2 × 24 = 48.