Lena has 6 errands to run this week, and she would like to take care of 2 of them today. In how many sequences could she run any 2 of the errands today? sequencesSubmit
Question
Lena has 6 errands to run this week, and she would like to take care of 2 of them today. In how many sequences could she run any 2 of the errands today? sequencesSubmit
Solution
This is a combination problem. Lena has 6 errands and she wants to choose 2 of them. The order in which she does them doesn't matter.
The formula for combinations is:
C(n, r) = n! / [r!(n - r)!]
where:
- n is the total number of options,
- r is the number of options chosen at a time,
- "!" denotes a factorial, meaning the product of all positive integers up to that number.
Substituting the given values into the formula:
C(6, 2) = 6! / [2!(6 - 2)!]
This simplifies to:
C(6, 2) = (654321) / [(21) * (432*1)]
After simplifying, we get:
C(6, 2) = (720) / (2 * 24)
C(6, 2) = 720 / 48
C(6, 2) = 15
So, Lena could run her errands in 15 different sequences.
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