FCP
A smoothie bar offers 3 cup sizes, 4 fruit choices, and 2 protein additives. How many different single-flavor smoothies with one protein additive can be ordered?
24
Evaluate 6!
720
Evaluate the permutations expression: 8P3
336
Evaluate the combinations expression: 10C3
120
A coach picks 3 team captains out of 15 players (with no specific roles). Does this require permutations or combinations, and how many ways can they be selected?
455
A student creates a 4-digit security PIN using the digits 0 through 9. How many different PINs are possible if repetition of digits is allowed?
10000
Evaluate
(12!)/(10!2!)
66
How many unique 5-letter permutations can be formed using all the letters in the word PLANT if the letter "P" must be in the first position?
24
A book club has 12 members. In how many ways can a 4-person reading committee be chosen where order does not matter? Use combinations.
495
A track relay team needs 4 runners chosen from 10 athletes to run specific legs (1st, 2nd, 3rd, and 4th leg). Does this require permutations or combinations, and how many ways can the team be assigned?
5040
How many ways are there to draw a single card from a standard 52-card deck that is either a Heart or an Ace?
16
Simply and expand
((n+2)!)/(n!)
n^2+3n+2
How many distinct identical-item permutations of the letters in the word REPETITION can be formed?
453 600
Out of 5 engineers and 6 architects, how many different 4-person project teams can be formed containing exactly 2 engineers and 2 architects using combinations?
150
In how many ways can 8 camp counselors be assigned to sleep in 3 cabins that hold 3, 3, and 2 counselors respectively? Use combinations.
560
A license plate consists of 3 letters followed by 3 digits. How many different license plates can be created if the first letter must be a vowel (A, E, I, O, U) and repetition of letters and digits is not allowed?
2 160 000
Express (n+5)(n+4)! as a single concise factorial expression.
(n+5)!
In how many ways can 4 boys and 3 girls sit in a row of 7 chairs if all 3 girls must sit together in a block? Express your steps using permutations.
720
A pizza shop offers 8 different toppings. How many different topping combinations can be created for a pizza with at least 1 topping?
255
A student council of 10 people (including Sarah) chooses a 3-person executive committee (President, Vice-President, Secretary). How many executive permutations are possible if Sarah must be President?
72
A license plate consists of 3 letters followed by 3 digits. How many different license plates can be created if the first letter must be a vowel (A, E, I, O, U) and repetition of letters and digits is not allowed?
36+9=45
Solve the factorial equation for n:
((n+1)!)/((n-1)!)=56
n=7
A robot moves on a grid from (0,0) to (5,3) by only moving East (E) or North (N). How many unique grid pathway permutations exist?
56
From a group of 4 men and 5 women, a committee of 4 people is to be chosen. How many committee combinations contain at least 1 man?
121
A committee of 5 is chosen from 6 teachers and 4 students. How many committee combinations can be formed if the committee must contain at most 1 student?