Permutation Formula, QnA

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 1st, 2nd, 3rd 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 1st champion, means there are 7 ways to determine the 1st champion, then 6 participants is left to be the 2nd champion, its means there are 6 ways to determine the 2nd champion. If we have got the 1st and 2nd champion, then there ar 5 participants is left to be the 3rd champion, its means there are 5 ways to determine the 3rd champion. Based on the reduplication rule, then the possible arrangement that occupy the champion 1st, 2nd and 3rd =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 1st, 2nd, and, 3rd champion which are taken from 7 participants who follow the championship. The arrangement of the 1st, 2nd and 3rd 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:
7P3 or P(7,3) or P7,3 or P37
Pay attention that: P37=7∙6∙5, that can be changed into:

using permutation

Which means:
use permutation

If n and k is positive integerwith n≥k then permutation formula:
permutation formula

QnA about permutation. Exercise Competency Test 6
1. The value of 7P3 is equal to …
A. 840 B. 280 C. 210 D. 70 E. 35
Answer: C, explanation:
permutation is

2. The value of 10P2 is equal to …
A. 90 B. 45 C. 35 D. 20 E. 15
Answer: A, explanation:

permutation math

3. The value of 13P3 is equal to …
A. 1716 B. 1617 C. 6171 D. 156 E. 155
Answer: A, explanation:

qna permutation

4. The value of (7P36P2)=⋯
A. 210 B. 200 C. 190 D. 180 E. 170
Answer: D, explanation:

permutation qna

5. The value of n to make nP2 is …
A. 9 B. 8 C. 7 D. 6 E. 5
Answer: A, explanation:

permutation form

6. The value of n to make n-1P2 is …
A. 12 B. 11 C. 10 D. 9 E. 6
Answer: A, explanation:

value of n in permutation

7. If n+1P3=nP4 then n=⋯
A. 2 B. 3 C. 4 D. 5 E. 6
Answer: D, explanation:

using permutation formula

8. If 2n+1P2nP3=0 then n=⋯
A. 4 B. 5 C. 6 D. 7 E. 8
Answer: D, explanation:

problem solving of permutation


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