Question

Fan, medal, and testimonial if you help me with this problem!!

How many numbers between 250 and 700 can be formed by using 2, 3, 4, 5, 6 with no repeats?

My answer 66?? I need help on the steps

Answer 1

@jim_thompson5910 @mathmate @mathscience4ever @mathstudent55

Answer 2

Focusing on just 3, 4, 5, 6 for the first digit, we have 4 choices for slot 1

That leaves 5-1 = 4 digits left over for slot 2
and 5-2 = 3 digits for slot 3

4*4*3 = 16*3 = 48 different 3 digit numbers that start with 3,4,5, or 6

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if we have 2 in the first slot, then we can't have 3 or 4 in the second slot. Only 5 or 6 can be picked. That leaves 3 digits left over

1*2*3 = 6

there are 6 different permutations that start with 2 and are larger than 250

they are...

253
254
256
263
264
265

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in total, there are 48+6 = 54 different numbers that are between 250 and 700

Answer 3

could you explain how you got 6 permutations?