CBSE - Class 11 Mathematics Permutations and Combinations Worksheet
1.
How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if. (i) 4 letters are used at a time,
2.
In how many of the distinct permutations of the letters in MISSISSIPPI do the four $I$'s not come together?
3.
A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: (ii) atleast 3 girls ?
4.
How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?
5.
If the different permutations of all the letter of the word EXAMINATION are listed as in a dictionary, how many words are there in this list before the first word starting with E ?
6.
From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen ?
7.
Evaluate (ii) $4! – 3!$
8.
Find $r$ if (ii) ${}^5P_r = {}^6P_{r-1}$.
9.
In how many ways can the letters of the word PERMUTATIONS be arranged if the (i) words start with P and end with S,
10.
It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible ?
11.
Evaluate (i) $8!$
12.
How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated ?
13.
In how many ways can the letters of the word PERMUTATIONS be arranged if the (ii) vowels are all together,
14.
The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet ?
15.
How many 5-digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once?
16.
How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that (i) repetition of the digits is allowed?
17.
Evaluate $frac{n!}{(n-r)!}$, when (i) $n = 6, r = 2$
18.
In how many ways can the letters of the word ASSASSINATION be arranged so that all the $S$'s are together ?
19.
Determine $n$ if (ii) ${}^{2n}C_3 : {}^nC_3 = 11 : 1$
20.
In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?
