Permutation and Combination- Key Notes
Permutation and Combination-
- Permutation and
Combination Aptitude basics, practice questions, answers and
Prepare for companies tests and interviews
nPr = n!/
nCr = nC(n-r)
nCr = nPr/r!
1. How many words can be formed by
re-arranging the letters of the word ASCENT such that A and T occupy the first
and last position respectively?
C)6! - 2!
D)6! / 2!
2. There are 2 brothers among a group of
20 persons. In how many ways can the group be arranged around a circle so that
there is exactly one person between the two brothers?
A) 2 *
C) 19! *
D)2 * 18!
3. There are 12 yes or no questions. How
many ways can these be answered?
4. How many ways can 4 prizes be given
away to 3 boys, if each boy is eligible for all the prizes?
D) None of these
5. A team of 8 students goes on an
excursion, in two cars, of which one can seat 5 and the other only 4. In how
many ways can they travel?
6. How many numbers are there between
100 and 1000 such that at least one of their digits is 6?
7. How many ways can 10 letters be
posted in 5 post boxes, if each of the post boxes can take more than 10
8. In how many ways can the letters of
the word EDUCATION be rearranged so that the relative position of the vowels
and consonants remain the same as in the word EDUCATION?
D) None of these
9. In how many ways can 15 people be
seated around two round tables with seating capacities of 7 and 8 people?
10. If the letters of the word CHASM are
rearranged to form 5 letter words such that none of the word repeat and the
results arranged in ascending order as in a dictionary what is the rank of the
11. How many words of 4 consonants and 3
vowels can be made from 12 consonants and 4 vowels, if all the letters are
A) 16C7 * 7!
B) 12C4 * 4C3 * 7!
C) 12C3 * 4C4
D) 12C4 * 4C3
12. In how many ways can 5 letters be
posted in 3 post boxes, if any number of letters can be posted in all of the
three post boxes?
13. How many number of times will the
digit '7' be written when listing the integers from 1 to 1000?
14. There are 6 boxes numbered 1,
2,...6. Each box is to be filled up either with a red or a green ball in such a
way that at least 1 box contains a green ball and the boxes containing green
balls are consecutively numbered. The total number of ways in which this can be
15. What is the value of 1*1! + 2*2! +
3!*3! + ............ n*n!, where n! means n factorial or n(n-A(n-2)...1
C) (n+A! - n!) D) (n + A! - 1!)
1.B; 2.D; 3.C; 4.C; 5.C; 6.D; 7.A; 8.C;
9.C; 10.C; 11.B; 12.D; 13.B; 14.B; 15.D