# Hotmath

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.

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

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

*x*!)

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

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

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

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.