Question

Circular Permutations and Permutations with Similar Elements

1) In how many ways can three people be made to sit at a round table?

2) In how many ways can three couples be seated at a round table, so that men and women sit alternately?

3) In how many ways can five keys be put on a key ring?

4) Find the number of different permutations of the letters of the word MATHEMATICS.

5) How many different ways can three pennies, two nickels and five dimes be arranged in a row?

6) How many five-digit numbers can be made using two 6's and three 7's?

7) If a coin is tossed 10 times, how many different outcomes of 7 heads, and 3 tails are possible?

8) If a team plays ten games, how many different ways can the team have a winning season?

Answer #1

How many ways can n student, n teacher and n parent be arranged
along a table of size 3n if they must be seated alternately and the
first seat (from the left) be allotted to a teacher?
Observe that the alternate seating requirement essentially means
that any 3 consecutive seats must have all different people seated
in them.

Permutations---------
In how many distinct ways can all the letters of the word
UNBELIEVABLE be arranged amongst themselves if
a) there are no restrictions?
b) the arrangement begins with the letters I V A, in that
order?
c) the arrangements must begin and end with a consonant?

A) How many permutations of 7 objects, taking 3 at a time?
Group of answer choices: 210, 35, 5040, 6
B) How many ways can 4 books be arranged on a shelf, if they can
be selected from 12 books?
C) How many ways can a committee of 4 people be selected from a
group of 8 people?
D) If the letters A, B, C, D, E, and F are to be used in a
five-letter code, how many different...

How many:
ways can an exam consisting of 10 true and false questions be
answered?
ways can an exam consisting of 5 true and false questions
followed by 2 multiple choice questions with four choices each be
answered?
4-digit numbers are there?
New York license plates can be made that consist of 3 letters
followed by 4 numbers?
New York license plates can be made that consist of 3 letters
followed by 4 numbers given the restriction that if the...

1. How many permutations are there of the letters in the word
RINSE, if all the letters are used without repetition?
2. In how many distinct ways can the letters of the word SELLS
be arranged?

in how many ways can six people, a,b,c,d,e and f, be
seated in a row such that a and b must sit together and c and d
must never sit together?

in how many different ways can the digit 0 to 5 be
arranged three at a time?

There are 18 empty chairs in a room. How many different ways can
4 people be seated in the room?

In how many ways can 4 mathematics books, 3 physics books, and
2 chemistry books be arranged on a bookshelf if
a) the books can be arranged in any order ?
b) the mathematics books must be together, the physics books
must be together, and
the chemistry books must be together ?
c) the mathematics books must be together, but the other books
can be arranged in
any order ?

Suppose that a cookie shop has three different kinds of cookies.
How many different ways can five cookies be chosen?

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