Find the value of r such that {^{8}P_r} = 6720. — JAMB UTME

Find the value of $r$ such that ${^{8}P_r} = 6720$ .

Cevap: 5

The value of

r

is 5.

Expanding

{^{8}P_r}

into consecutive decreasing factors starting from 8 yields

8 \times 7 \times 6 \times 5 \times 4 = 6720

. Counting the number of factors multiplied (8, 7, 6, 5, 4) gives exactly 5 factors, so

r = 5

Write the formula for permutation

{^{8}P_r}

as a product of descending integers.

{^{8}P_r} = 8 \times 7 \times 6 \times \dots \times (8 - r + 1)

By definition,

{^{n}P_r}

represents the product of

r

consecutive factors starting from

n

and decreasing by 1.

Perform sequential multiplication starting from 8 until reaching 6720.

Product of 5 factors:

8 \times 7 \times 6 \times 5 \times 4 = 6720

Multiplying factors gives:

8 \times 7 = 56

;

56 \times 6 = 336

;

336 \times 5 = 1680

;

1680 \times 4 = 6720

Count the number of terms in the product to find

r

r = 5

Since 5 consecutive integers were multiplied together to obtain 6720, the subset size

r

is 5.

Permutations of

n

distinct items taken

r

at a time

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