SOLUTION: Five different digits 7 3 6 2 5 are given. Out of these digits, 4 digits numbers are formed. Find the no. of 4-digit numbers formed which have at least one digit repeated.
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Question 935448: Five different digits 7 3 6 2 5 are given. Out of these digits, 4 digits numbers are formed. Find the no. of 4-digit numbers formed which have at least one digit repeated. Answer by Edwin McCravy(20054) (Show Source):
First find the number of four-digit numbers.
5 ways to pick the 1st digit.
5 ways to pick the 2nd digit.
5 ways to pick the 3rd digit.
5 ways to pick the 4th digit.
That's 5×5×5×5 = 54 = 625 four digit numbers altogether.
We need to subtract from that the number of four-digit numbers
which have no digit repeated.
5 wasy to pick the 1st digit.
4 ways remaining to pick the 2nd digit.
3 ways remaining to pick the 3rd digit.
2 ways rewmaining to pick the 4th digit.
That's 5×4×3×2 = 5! = 120 four digit numbers with no digits repeated.
Answer: 625-120 = 505.
Edwin
