The formula for the number of all permutations of n things taken r at a time is given by ___ .

NPr = n! / (n - r)!

True or False: The factorial of a negative number is a valid expression.

False. Factorial of any negative quantity is not valid.

In permutations, when repetition is allowed, the number of arrangements of n different things taken r at a time is given by ___ .

N^r

Fill in the blank: The number of combinations of n things taken r at a time is represented by ___ .

NCr

What is the value of 0!?

1

Riddle: I am the arrangement of objects, and my value increases as you take more at a time. What am I?

Permutations

If n is odd, to maximize nCr, r should be ___ .

(n - 1)/2

The combination formula nCr can be expressed in terms of permutations as ___ .

NCr = nPr / r!

True or False: The sum of combinations from nC0 to nCn equals 2^n.

True.

If from a total set of n objects, p1 are of one kind and p2 are of another kind, the formula for permutations is given by ___ .

N! / (p1! * p2! * ... * pr!)

What is the factorial of 5?

120

Fill in the blank: The total number of ways to arrange n different things taken all at a time is ___ .

N!

In the case of distributing k balls into n boxes, the conditions can include that no box may contain more than one ball or ___ .

Any box may contain more than one ball.

Riddle: I can be arranged in different orders, but my total number remains unchanged when you select all. What am I?

Permutations

For n = 5 and r = 3, calculate nPr.

60

Fill in the blank: The number of ways to select r things from n things is given by ___ .

NCr

What is the relationship between nCr and nCr-1?

NCr + nCr-1 = n+1Cr

True or False: The value of nCr is maximum when r = n/2 if n is even.

True.

In permutations, if the same object can be used more than once, the formula simplifies to ___ .

N^r

What is the value of 5!?

120