Combinations and Permutations MDM4U

At the co-ed volleyball team try-outs, 15 girls and 8 boys show up. In how many ways can the coach create the team of 10 players if there must be exactly 5 girls and 5 boys on the team?

• P(15,5)×P(8,5)

• C(23,10)

• C(15,5)×C(8,5)

• P(23,5)/(5!5!)

Joanna works at a bakery shop that has 8 different colours of sprinkles. How many different combinations of colours can customers choose to have on their cake if can choose at most 5 types?

• 218

• 219

• 256

• 255

In how many ways can you arrange 10 markers in a row if there are 4 blue markers, 2 green, 3 yellow and 1 red?

How many permutations are there of all the letters in the word BRONTECOLLEGE?

• 6,227,020,800
• 259,459,200

• 518,918,400

• 129,729,600

From a standard deck, how many four-card hands contain only red cards?

• 26!/4!

• C(26,4)

• P(26,4)

• P(13,2)×P(13,2)

Abuela is making a vegetable stew using 7 different possible vegetables. How many different combinations of vegetables can she put in the stew if she is using at least 1 vegetable?

• 8

• 128

• 127
• 120

There’s an upcoming Mathletes competition and there are 5 teachers interested in going and 16 students. In how many ways can the group of 10 people be made if there must be at least 2 teachers?

• 158,808

• 287,508

• 128,700

• 193,908

How many ways can 6 friends sit around a table if Elsa and Anna cannot sit beside each other?

• 72

• 120

• 48

• 96

A group of students volunteer at a retirement community. From 10 students and 12 senior citizens, if 5 students and 5 senior citizens are to be chosen and then paired off to spend the day together, in how many ways can this be done?

• C(10,5)×C(12,5)

• P(10,5)×P(12,5)

• C(10,5)×C(12,5)×2⁵

• C(10,5)×C(12,5)×5!

From a classroom with 17 students, 6 are selected to form a group. How many ways can this be done so that either Johnathan or Scott (but not both) are in the group?

• C(2,1)×C(15,5)

• C(17,6)-C(2,2)×C(15,6)

• P(17,6)-P(2,2)×P(15,6)