Permutations and combinations

Answer Key - Grade 11 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   Noah's student council picks 2 of 7 seventh graders and 2 of 6 eighth graders. How many different councils of 4 are possible?

   315
2. 2.

   Pia picks 2 of 6 vegetable toppings and 1 of 3 cheeses for a pizza. How many different pizzas are possible?

   45
3. 3.

   Tala picks 2 of 8 slow songs and 3 of 6 fast songs for a music mix, in no set order. How many different mixes are possible?

   560
4. 4.

   Zee's team of 9 picks a captain, then 3 more players from the rest for a skills show. How many ways can this be done?

   504
5. 5.

   Bo's class of 10 picks a leader, then a 2-person crew from the rest, to run the book swap. How many ways are possible?

   360
6. 6.

   Esme's group of 8 campers picks a tent leader, then 4 tent mates from the rest. How many ways are possible?

   280
7. 7.

   Jun's band of 12 picks a soloist, then a 3-person backup group from the rest. How many ways are possible?

   1980
8. 8.

   Kira's class of 25 picks a book committee of 4. Using a calculator, how many different committees are possible?

   12650
9. 9.

   Luz's club of 20 elects a president, vice president, secretary and treasurer, one job each. Using a calculator, how many ways can the jobs be filled?

   116280
10. 10.

    Noah's race has 18 runners, and the top 5 places get ribbons. Using a calculator, how many ways can the 5 ribbons be given?

    1028160