If one event can occur in m ways and a second thing can occur in n ways, then which expression gives the number of ways both events can occur?

Which expression is equivalent to 𝑛!?

It is referred to as an arrangement of things in definite order or distinct arrangement of distinguishable objects.

A coat hanger has four knobs, and each knob is to be painted by a distinct color. If six different colors of paint are available, how many ways can the knobs be painted?

Evaluate P(7, 5).

A new model of a car is available in six exterior colors, three interior colors, and two interior styles. How many versions of car are available for order?

A multiple-choice test contains five questions, and each question has four options. In how many ways can the five questions be answered?

A bookshelf has five different Algebra books and n different Geometry books. If there are 40 320 ways to arrange the books on the shelf, how many Geometry books are on the bookshelf?

How many ways can the letters from the word FLEA be arranged such that each “word” starts with a consonant and ends with a vowel?

How many three-digit numbers can be formed using the digits 5, 7, 8 and 2 if the digits cannot be repeated?

How many three-digit numbers can be formed using the digits 5, 7, 8 and 2 if repetition of digits is not allowed, and the number is less than 700?

How many three-digit numbers can be formed using the digits 5, 7, 8 and 2 if 5 is the first digit and repetition is not allowed?

How many three-digit numbers can be formed using the digits 5, 7, 8 and 2 if 5 is the first digit, 2 is the second digit, and repetition of digits is allowed?

How many three-digit numbers can be formed using the digits 5, 7, 8 and 2 if 5 is the first digit, 2 is the last digit, and repetition of digits is not allowed?

How many permutations are there in the letters of the word HELPING if ING remain in that order?

What concept is involved when the letters of the word “FAIR” taken 4 at a time equals 24?

In how many ways the letters of the word “RUNNING” be arranged?

There are four identical green flags, two identical white flags, and two identical red flags. Using all eight flags, how many signals can be made?

How many six-digit numbers can be made using the digits from 9, 4, 4, 3, 4, and 2?

A department store sells three same jackets, three same shirts, two same ties, and two same pairs of pants. How many different suits consisting of jacket, shirt, tie, and pants are possible?

How many different ten-digit numerals can be written using the digits 1, 2, 3, 4, 4, 5, 5, 6, 6, and 9?

Find the number of distinguishable permutations of the letters of the word “ATI-ATIHAN”.

In how many ways can three identical issues of a Mathematics magazine, two identical Statistics magazine, and five identical Science magazine be put in a stack?

In how many ways can eight people be seated around a circular table?

How many ways can 11 people be seated around a circular table if two insist to seat next to each other?

Six keys, no two of which are the same, are to be placed on a circular key chain. How many different arrangements are there?

Seven beads, no two of which are the same, will be put together to form a bracelet without a lock. How many ways can the beads be arranged?

How many ways can eight beads, no two of which are the same, be arranged on a chain with a clasp?

Nine people are to be seated at a roundtable. One of them is to be seated close to the door. How many arrangements are possible?

In how many ways can five people be seated in a round table?