Multiple Choice
How many possible outcomes are there if you roll 5 dice?
10. Combinatorics & Probability
Combinatorics
Struggling with College Algebra?
Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
Emily is organizing her closet. She has 15 shirts left to hang but has space in one section for 6 shirts. How many ways could she hang shirts in that section?
A
3,603,600
B
90
C
9
D
362,880
Verified step by step guidance1
Identify the problem as a permutation problem where Emily needs to select and arrange 6 shirts out of 15.
Recall the formula for permutations: \( P(n, r) = \frac{n!}{(n-r)!} \), where \( n \) is the total number of items to choose from, and \( r \) is the number of items to arrange.
Substitute \( n = 15 \) and \( r = 6 \) into the permutation formula: \( P(15, 6) = \frac{15!}{(15-6)!} \).
Calculate \( 15! \) (15 factorial), which is the product of all positive integers up to 15.
Calculate \( 9! \) (9 factorial), which is the product of all positive integers up to 9, and then divide \( 15! \) by \( 9! \) to find the number of permutations.
4:4mWatch next
Master Fundamental Counting Principle with a bite sized video explanation from Patrick
Start learningRelated Videos
Related Practice
