Question
Pashmina has 13 apps on her phone. Calculate the number of ways Pashmina can choose 2 of her favorite apps from the 13 on her phone.(1 point) Responses 813 8 Start Fraction 1 over 3 End Fraction 3,113,510,400 3,113,510,400 78 78 156
Answers
GPT-4o mini
To calculate the number of ways Pashmina can choose 2 favorite apps from 13, we use the combination formula:
\[
\binom{n}{r} = \frac{n!}{r!(n-r)!}
\]
where \( n \) is the total number of items to choose from, \( r \) is the number of items to choose, and \( ! \) denotes factorial, which is the product of all positive integers up to that number.
For this problem, \( n = 13 \) and \( r = 2 \):
\[
\binom{13}{2} = \frac{13!}{2!(13-2)!} = \frac{13!}{2! \cdot 11!}
\]
The factorials can be simplified:
\[
\binom{13}{2} = \frac{13 \times 12 \times 11!}{2! \times 11!}
\]
The \( 11! \) cancels out:
\[
\binom{13}{2} = \frac{13 \times 12}{2!} = \frac{13 \times 12}{2}
\]
Now, calculating further:
\[
= \frac{156}{2} = 78
\]
Thus, the number of ways Pashmina can choose 2 favorite apps is \( \boxed{78} \).
\[
\binom{n}{r} = \frac{n!}{r!(n-r)!}
\]
where \( n \) is the total number of items to choose from, \( r \) is the number of items to choose, and \( ! \) denotes factorial, which is the product of all positive integers up to that number.
For this problem, \( n = 13 \) and \( r = 2 \):
\[
\binom{13}{2} = \frac{13!}{2!(13-2)!} = \frac{13!}{2! \cdot 11!}
\]
The factorials can be simplified:
\[
\binom{13}{2} = \frac{13 \times 12 \times 11!}{2! \times 11!}
\]
The \( 11! \) cancels out:
\[
\binom{13}{2} = \frac{13 \times 12}{2!} = \frac{13 \times 12}{2}
\]
Now, calculating further:
\[
= \frac{156}{2} = 78
\]
Thus, the number of ways Pashmina can choose 2 favorite apps is \( \boxed{78} \).