Prime numbers 2 through 100 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97. Even numbers greater than two are composite.

5 0

3 years ago

A police department in a small city consists of 10 officers. If the department policy is to have 5 of the officers patrolling th

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Answer:

2,520

Step-by-step explanation:

The number of possible arrangements of officers patrolling the streets is the combination of choosing 5 officers out of 10 (₁₀C₅). After choosing the patrolling officers, the number of arrangements for the officers working full time at the station is given by the combination of choosing 2 officers out of the 5 remaining (₅C₂). The remaining officers should be on reserve at the station (₃C₃). The total number of arrangements is:

$N = _{10}C_5*_5C_2*_3C_3\\N=\frac{10!}{(10-5)!5!} *\frac{5!}{(5-2)!2!}*\frac{3!}{(3-3)!3!} \\N=2,520$

There are 2,520 possible divisions.

5 0

3 years ago