Mjcheyidn
Answered

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What is the value of 9P5?

A. 45
B. 126
C. 15,120
D . 59,049

A cooking club has 12 members.How many ways can they select a president and vice president from among the members?
A. 1320
B. 220
C. 132
D. 66

Sagot :

Kate200468idn
[tex]9\ P\ 5= \frac{9!}{(9-5)!} = \frac{9\cdot8\cdot7\cdot6\cdot5\cdot4!}{4!} =15120\ \ \ \Rightarrow\ \ \ Ans.\ C\\ \\ \\ \left ( {{12} \atop {2}} \right) \cdot2!= \frac{12!}{2!\cdot10!}\cdot2= \frac{12\cdot11\cdot10!}{2\cdot10!}\cdot2 =132\ \ \ \Rightarrow\ \ \ Ans.\ C[/tex]
The correct answers are:
C) 15120
C) 132.

Explanation:
9P5 is a permutation of 9 objects taken 5 at a time; this is
9! / (9-5)! = 9!/4!
                = (9*8*7*6*5*4*3*2*1)/(4*3*2*1)
                = 15120.

The second question is a permutation of 12 objects taken 2 at a time; this is 12! / (12-2)! = 12!/10!
                    =(12*11*10*9*8*7*6*5*4*3*2*1) / (10*9*8*7*6*5*4*3*2*1)
                    =132
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