Evaluate the expression 6!.

Find the value of 15!

Simplify the following:

7! 7

Evaluate:

Simplify.

( k + 3)!( k + 4)

Determine whether the given statement is true or false, and give a counterexample if the statement is false:

If x and y are positive integers determine whether the statement x ! – y ! = y ! – x ! is true or false. If the statement is true, explain. If the statement is false, give a counterexample.

(5 x )! = 5 ^{ x } ( x !)

Evaluate the expression _{ 9 } P _{ 1 } .

Evaluate the expression _{ 7 } P _{ 4 } .

_{ 8 } C _{ 4 }

_{ 12 } C _{ 9 }

Which is greater?

Solve:

A group of students standing in a row. State whether this is a permutation or a combination.

Rajesh ordered five items from a menu in a restaurant. State whether this is a permutation or a combination.

Obtain the number of permutations possible for the group of letters shown. Use all the letters.

F, I, V, E

Obtain the number of three–letter permutations possible for the group of letters shown.

S, E, V, E, N

Find the number of combinations using two different letters that can be formed from the group of letters by listing the combinations.

F, O, U, R

In how many different ways can the letters of the word EXPRESSION be arranged?

How many number of 6–letter permutations be formed from the letters in the word FLUBBER?

A choir of 10 students have to be chosen from a class of 17. State whether this is a permutation or a combination and find the number of ways it can be done.

Check whether the given arrangement is linear or circular. Check if the given arrangement is also a reflection and find the number of arrangements.

A basketball huddle of 7 players

9 pizza toppings placed on a revolving tray.

Stephen has to pick 5 fruits from the set of fruits

{apple, banana, mango, orange, peach, strawberry).

Find the number of combinations.

5 students from 100 participants have to be chosen for the International Mathematics Olympiad team. Find the number of combinations.

How many 13–card hands with exactly 11 spades can be dealt?

How many 6–card hands having exactly 3 aces and 3 other cards can be dealt? (Assume you have a regular 52–card deck.)

Find in how many ways can one select 5 or more students from 9 students?

Get the number of possible 6–card hands that contain the cards 4 jacks and 2 other cards.