Question
How many ways can you arrange 2 letters from the word S Q U A R E?
(1 Point)
30
45
140
320
(1 Point)
30
45
140
320
Answers
Answered by
GPT-4o mini
To determine how many ways we can arrange 2 letters from the word "SQUARE", we first recognize that "SQUARE" contains 6 distinct letters: S, Q, U, A, R, E.
The number of ways to choose 2 letters from these 6 letters and then arrange them can be found using the formula for permutations of n items taken r at a time, given by:
\[
P(n, r) = \frac{n!}{(n - r)!}
\]
where \( n \) is the total number of items (here, 6 letters) and \( r \) is the number of items to arrange (here, 2 letters).
Substituting the values into the formula:
\[
P(6, 2) = \frac{6!}{(6 - 2)!} = \frac{6!}{4!}
\]
Calculating \( 6! \) and \( 4! \):
\[
6! = 6 \times 5 \times 4! = 30 \times 4!
\]
So, \( P(6, 2) \) simplifies to:
\[
P(6, 2) = \frac{30 \times 4!}{4!} = 30
\]
Thus, the number of ways to arrange 2 letters from "SQUARE" is:
\[
\boxed{30}
\]
The number of ways to choose 2 letters from these 6 letters and then arrange them can be found using the formula for permutations of n items taken r at a time, given by:
\[
P(n, r) = \frac{n!}{(n - r)!}
\]
where \( n \) is the total number of items (here, 6 letters) and \( r \) is the number of items to arrange (here, 2 letters).
Substituting the values into the formula:
\[
P(6, 2) = \frac{6!}{(6 - 2)!} = \frac{6!}{4!}
\]
Calculating \( 6! \) and \( 4! \):
\[
6! = 6 \times 5 \times 4! = 30 \times 4!
\]
So, \( P(6, 2) \) simplifies to:
\[
P(6, 2) = \frac{30 \times 4!}{4!} = 30
\]
Thus, the number of ways to arrange 2 letters from "SQUARE" is:
\[
\boxed{30}
\]