Question 134503: how many four-digit numbers starting with 1 and ending with 5 can be written if the digits 1 2 3 4 5 6 7 8 9 are used, including the cases when a digit may appear twice in a given number?
Answer by edjones(8007)   (Show Source):
You can put this solution on YOUR website! All we have to know is how many ways can 2 (the middle 2) out of 9 numbers be arranged. The order is important so we do a permutation.
nPr=n!/(n-r)!
=9!/(9-2)!
=9*8*7!/7!
=72
72+9 (for the cases where the digit may appear twice)
=81
So, there are 81 four digit numbers starting with 1 and ending with 5.
1115, 1125, 1215, 1225, 1135, 1315, 1325, 1235, 1335, only 72 more to go!
.
Ed
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