Maths · Simple applications
The number of six-digit numbers that can be formed from the digits 1,2,3,4,5,6 a
The number of six-digit numbers that can be formed from the digits 1,2,3,4,5,6 and 7 so that digits do not repeat and the terminal digits are even is
- A. 144
- B. 72
- C. 288
- D. 720
Step-by-step solution
We need six-digit numbers from digits 1-7 without repetition, with first and last digits even. There are 3 even digits (2,4,6). Choose two distinct evens for the terminal positions: 3P2 = 6 ways. After fixing ends, 5 digits remain (1 odd, 3 odd? Actually 4 odds and 1 even). We need to fill the middle 4 positions with 4 of these 5 digits: number of ways = 5P4 = 120. Total = 6 × 120 = 720.
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