EXERCISE
- PERMUTATION
1. Find
the total number of different permutations of all the letters of the word
a) SIMPLE
b) SECONDARY
2. In
a survey, 10 characteristic of teacher are listed. You are asked to indicate in
order of importance of which 4 of these characteristic make a good teacher. How
many possible responses are there?
3. Amy,
Brian, Cheryl, Danny and Eric went to a concert. How many arrangement are
possible when they sit in five adjacent seats if
a) Eric
insists on sitting next to Cheryl?
b) Brian
Refuses Sitting next to Danny?
4. 9
different books are to be arranged on a bookshelf. 4 of these books were
written by Shakespeare, 2 by Dickens and 3 by Conrad. How many possible
permutations are there if
a) The
books by Conrad must be next to each other?
b) The
books by Dickens are separate from each other?
c) The
books by Conrad are separate from each other?
5. In
how many ways can a judge award first, second and third prizes in a contest
with 9 participants?
EXERCISE
- COMBINATION
1. In
a soccer league consisting of twelve sides, each team plays every other team
once. How many matches are there?
2. A
club has 14 members. It has to send delegation of 5 members to represent them
at a particular event. Find the number of possible delegations.
3. Seven
points lie on a circle. How many triangles can be drawn using any 3 of these
points as vertices?
4. Find
different letters are chosen from the letter A, B, C, D, E, F, G, H, I and J.
Find the number of choices. How many of these choices contain:
a) Exactly
3 consonants,
b) No
vowels,
c) At
least one vowel?
5. A
chess club has 10 members of whom 6 are men and 4 are women. A team of 4
members is selected to play in match. Find the number of different ways of
selecting the team if:
a) All
the players are to be of the gender,
b) There
must be an equal number of men and women.
Given
that the 6 men include 2 brothers, find the total numbers of ways in which the
team can be selected if either of the brothers, but not both, must be included.
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