Jamaal is heading to the beach for a vacation next week, and its time to pack. He has 6 pairs of swim trunks, but hell only need 3 for the trip. How many aitterent combinations of 3 pairs of trunks can he make?
Jamaal can make 20 different combinations of 3 pairs of swim trunks.
To see why, we can use the formula for combinations, which is:
nCr = n! / r!(n-r)!
where n is the total number of items, r is the number of items to choose, and ! means factorial (the product of all positive integers up to that number).
In this case, n = 6 (the number of pairs of trunks that Jamaal has) and r = 3 (the number of pairs he needs to choose). So we can plug these values into the formula:
6C3 = 6! / 3!(6-3)!
= (6 x 5 x 4) / (3 x 2 x 1)
= 20
Therefore, Jamaal can make 20 different combinations of 3 pairs of swim trunks for his beach vacation.
To find the number of different combinations of 3 pairs of swim trunks that Jamaal can make, we can use the combination formula, which is:
nCr = n! / (r! * (n-r)!)
Where n is the total number of items, r is the number of items to be chosen, and ! denotes factorial (n! = n * (n-1) * (n-2) * ... * 2 * 1).
In this case, n is the number of swim trunks (6) and r is the number of trunks needed for the trip (3).
Let's calculate:
6! / (3! * (6-3)!) = 6! / (3! * 3!) = (6 * 5 * 4) / (3 * 2 * 1) = 20
Therefore, Jamaal can make 20 different combinations of 3 pairs of swim trunks for his trip.