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  • If the correct choice of 5 numbers (from 1 to 15) is made, a permutation lock will unlock. How many lock permutations are possible if no number is repeated?<st

If the correct choice of 5 numbers (from 1 to 15) is made, a permutation lock will unlock. How many lock permutations are possible if no number is repeated?

Option: 1

360360


Option: 2

320320


Option: 3

460460

 


Option: 4

420460


Answers (1)

best_answer

We have 15 digits and arrange four of them. We have  { }^{15} P_5 options.

\begin{aligned} & { }^{15} P_5=\frac{15 !}{(15-5) !} \\ & { }^{15} P_5=\frac{15 !}{10 !} \\ & { }^{15} P_5=\frac{15 \times 14 \times 13 \times 12 \times 11 \times 10 !}{10 !} \\ & { }^{15} P_5=15 \times 14 \times 13 \times 12 \times 11 \times 10 \\ & { }^{15} P_5=360360 \end{aligned}

 Therefore, the total number of ways lock permutations can be made in 360360 ways.

Posted by

jitender.kumar

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