Choose 3 digits from 3, 9, 8, 2, 6, 1 to form 3-digit numbers. How many even
numbers are there? (The repetition of digits is not allowed)
K
Khách
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27 tháng 8 2021
The Partial Permutations of N items taken K at a time is:
N! / (N - K)!
For N = 9 and K = 3, we get
9! / 6! = 7*8*9 = 504 possible three digit numbers.
Of those, odd are those which end in 1,3,5,7,9 (5 accepted endings) from a total of 1,2,3,4,5,6,7,8,9 (9 possible endings).
So, we take 5/9 of 504.
(5/9)*504 = 280.
Because the number is even, the units digit is even
There are 3 ways to select the unit digit
There are 5 ways to select the unit digit
There are 4 ways to select the unit digit
The number of satisfying numbers is:
3 × 5 × 4 = 60 (numbers)