+0

0
90
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How many ways can you arrange the digits 1, 2, 4, 5, 6, 7, to get a six-digit number that is divisible by 25?

May 7, 2020

#1
+50
0

for a number to be divisible by 25, it must end in either 00 (making it a multiple of 100), 25 (a multiple of 100 + 25), 50 (a multiple of 50), or 75 (a multiple of 100 + 75). since 0 isn't in our digits, the digits must be in the form

$$\times\times\times\times25$$

or

$$\times\times\times\times75$$

where $$\times$$ represents any digit not used. there are $$4!$$ ways to arrange the digits that fit the first form and $$4!$$ ways for the second, so we have a total of

$$4! + 4! = 24 + 24 =\boxed{48}$$

ways to arrange the digits.

May 7, 2020