**Permutation**

Sometimes the member of an event is the arrangement of a group of element which is taken from some elements which is provided. Suppose we want to determine the number of possible arrangements of the champion 1^{st}, 2^{nd}, 3^{rd} in a horse racing which is followed by 7 participants. To possible arrangement is surely different each other. The number of arrangements can be determined as the following.

All participants have possibility to the be 1^{st} champion, means there are 7 ways to determine the 1^{st} champion, then 6 participants is left to be the 2^{nd} champion, its means there are 6 ways to determine the 2^{nd} champion. If we have got the 1^{st} and 2^{nd} champion, then there ar 5 participants is left to be the 3^{rd} champion, its means there are 5 ways to determine the 3^{rd} champion. Based on the reduplication rule, then the possible arrangement that occupy the champion 1^{st}, 2^{nd} and 3^{rd} =7×6×5=210.

In determining the number of arrangements of champion position on the explanation above, we take 3 participants who will occupy the 1^{st}, 2^{nd}, and, 3^{rd} champion which are taken from 7 participants who follow the championship. The arrangement of the 1^{st}, 2^{nd} and 3^{rd} champion is called permutation. The number of possible arrangements is the number of permutation of the 3 objects which is taken from the 7 objects which are provided, and it is written by:

_{7}P_{3} or P(7,3) or P_{7,3} or P_{3}^{7}

Pay attention that: P_{3}^{7}=7∙6∙5, that can be changed into:

Which means:

If

*n*and

*k*is positive integerwith

*n≥k*then

**permutation formula**:

**QnA about permutation. Exercise Competency Test 6**

1. The value of

_{7}P

_{3}is equal to …

A. 840 B. 280 C. 210 D. 70 E. 35

Answer: C, explanation:

2. The value of _{10}P_{2} is equal to …

A. 90 B. 45 C. 35 D. 20 E. 15

Answer: A, explanation:

3. The value of _{13}P_{3} is equal to …

A. 1716 B. 1617 C. 6171 D. 156 E. 155

Answer: A, explanation:

4. The value of (_{7}P_{3}–_{6}P_{2})=⋯

A. 210 B. 200 C. 190 D. 180 E. 170

Answer: D, explanation:

5. The value of *n* to make _{n}P_{2} is …

A. 9 B. 8 C. 7 D. 6 E. 5

Answer: A, explanation:

6. The value of *n* to make _{n-1}P_{2} is …

A. 12 B. 11 C. 10 D. 9 E. 6

Answer: A, explanation:

7. If _{n+1}P_{3}=_{n}P_{4} then *n*=⋯

A. 2 B. 3 C. 4 D. 5 E. 6

Answer: D, explanation:

8. If _{2n+1}P_{2}–_{n}P_{3}=0 then *n*=⋯

A. 4 B. 5 C. 6 D. 7 E. 8

Answer: D, explanation: