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Ten students sit together. Reatlife-Problem
(a) In how many ways can they sit if they sit in a row?
10^(:):-3628800
(b) In how many ways can they sit if they sit in two rows with five seats each?
Hint 4

Ten students sit together. $\newline$ (a) In how many ways can they sit if they sit in a row? $\newline$ (b) In how many ways can they sit if they sit in two rows with five seats each?

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Add, subtract, multiply, and divide polynomials

Full solution

Q. Ten students sit together.

\newline

(a) In how many ways can they sit if they sit in a row?

\newline

(b) In how many ways can they sit if they sit in two rows with five seats each?

Calculate Ways in a Row: Calculate the number of ways to arrange ten students in a row. $\newline$ Using the formula for permutations, $n!$ , where $n$ is the number of students: $\newline$ $10! = 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 3628800$
Calculate Ways in Two Rows: Calculate the number of ways to arrange ten students in two rows of five each. $\newline$ First, choose $5$ students for the first row (combination), then arrange them (permutation). Repeat for the second row. $\newline$ Number of ways = $(10 \choose 5) \times 5! \times 5!$ $\newline$ = $(10! / (5! \times 5!)) \times 5! \times 5!$ $\newline$ = $10! / 5! = 30240$

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