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vagabundo [1.1K]
3 years ago
15

can anyone help me with this ??

Mathematics
1 answer:
Mars2501 [29]3 years ago
4 0

Answer:

A. 336

B. Arranging 3 people in 8 chairs.

C. 42

B. Arranging 2 people in 7 chairs.

Step-by-step explanation:

A.

P(n, r) = P(8, 3)

Formula for Permutation is given as:

P(n, r) = \dfrac{n!}{(n-r)!}

Putting the value of n = 8 and r =3 , we get:

P(8, 3) = \dfrac{8!}{(8-3)!} \\\Rightarrow \dfrac{8\times 7 \times 6 \times 5\times 4 \times 3 \times 2\times 1}{5\times 4 \times 3\times 2\times 1}\\\Rightarrow 8\times 7 \times 6 \\\Rightarrow 336

B. Real world situation for part A:

Arranging 3 people on 8 chairs.

First person has 8 options.

Second person has 7 options.

Third person has 6 options.

C.

P(n, r) = P(7, 2)

Formula for Permutation is given as:

P(n, r) = \dfrac{n!}{(n-r)!}

Putting the value of n = 7 and r = 2 , we get:

P(7, 2) = \dfrac{7!}{(7-2)!} \\\Rightarrow \dfrac{7 \times 6 \times 5\times 4 \times 3 \times 2\times 1}{5\times 4 \times 3\times 2\times 1}\\\Rightarrow 7 \times 6 \\\Rightarrow 42

D.  Real world situation for part AC:

Arranging 2 people on 7 chairs.

First person has 7 options.

Second person has 6 options.

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