Sonji bought a combination lock that opens with a four-digit number created using the digits 0 through 9. The same digit cannot be used more than once in the combination. If Sonji wants the last digit to be a 7 and the order of the digits matters, how many ways can the remaining digits be chosen? 84 504 3,024 60,

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23-05-2017
Mathematics

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Sonji bought a combination lock that opens with a four-digit number created using the digits 0 through 9. The same digit cannot be used more than once in the combination. If Sonji wants the last digit to be a 7 and the order of the digits matters, how many ways can the remaining digits be chosen? 84 504 3,024 60,

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nadelynp nadelynp · Answer 1 · 2017-05-30T21:49:49+02:00

Since it is a four combination lock or permutation and she wants the last digit to be seven we have_,_,_,7
The first digit: Since we need it to be any number except 7 we have 9 possibilities.For the second digit: We have 8 possibilities since the numbers can't be repeated and we already chose 7 to be the last digit and any other digit to be the first digit.For the third digit: there are 7 possibilities since we already chose three numbers and these cannot be repeated.
We have the following:9*8*7=504