Perms
How many ways can 5 different students line up for a photograph?
5!=120
How many ways can 2 students be selected from a group of 6?
6C2=15
What is 7!/6!
7
A restaurant offers 4 mains, 3 sides, and 5 drinks. How many meals can be made by choosing one of each?
4x3x5=60
3 digit numbers are formed using only the digits 2,3,5,6,7,9
If repetitions are not allowed, how many 3-digit numbers can be formed?
6x5x4= 120
A student must choose 4 electives from a list of 9. How many different course selections are possible?
9C4=126
What is 5P4? Do so algebraically and confirm with your calculator.
120
A student is choosing a 4-digit pin, selecting 5 students for a committee, and arranging 6 books on a shelf. Identify which situations involve permutations and which involve combinations.
Pin: permutation
Committee: combination
Book: permutation
How many different arrangements can be made using all the letters in BALLOON?
7!/ 2!2! =1260
A committee of 4 must contain exactly 2 boys and 2 girls. If there are 5 boys and 6 girls available, how many committees can be formed?
5C2 x 6C2 = 150
How many arrangements can be made of the word MOTHER if the vowels are first and last?
2x4x3x2x1x1 =48
A password consists of 3 digits (0–9). Digits may repeat. How many passwords are possible?
10x10x10= 1000
How many different arrangements can be made using the letters in SCHOOL if the first letter must be S?
5!/2!=60
A student must complete 5 courses. There are 11 to choose from. English is mandatory, and the other courses must be chosen from the other available options. How many different schedules of courses can be selected?
10C4= 210
Simplify:
(n!)/(n-1!) +2n
3n
A pizza shop offers 3 crusts, 2 cheeses, 8 toppings, and 4 sauces. How many pizzas can be made using one crust, one cheese, exactly 2 different toppings, and one sauce?
3C1 x 2C1 x 8C2 x 4C1 = 672
A bag contains 6 red marbles, 4 blue marbles, and 5 green marbles. Three marbles are randomly selected from the bag without replacement.
What is the probability that exactly 2 of the marbles are red?
6C2 x 9C1/15C3
135/455 = 30%
Seven friends go out to the movies. How many arrangements are possible if Clara, Mark, and Josh must sit together?
5!x3!=720
A school is selecting a committee of 6 students from a group of 7 girls and 5 boys. How many different committees can be formed if the committee must contain at least 4 girls?
4 girls, 2 boys: 7C4 x 5C2 = 350
5 girls, 1 boy: 7C5 x 5C1 = 105
6 girls, 0 boys: 7C6 x 5C0 =7
350+105+7=462
Solve:
(n-1!)/(n-3!) =20
n=6
Eight students volunteer for an event. Two will sell tickets, three will serve food, and the remaining three will clean up. How many different job assignments are possible?
8C2 x 6C3 x 3C3 = 20x28x1 =560
A school has 8 students interested in joining student council. Three students will be selected, and each will be assigned a different position: President, Vice-President, and Treasurer.
How many different ways can the students be selected and assigned their positions?
8C3= 56
3! =6
56x3!=336