CBSE - Class 11 Mathematics Permutations and Combinations Worksheet
1.
Evaluate $frac{n!}{(n-r)!}$, when (i) $n = 6, r = 2$
2.
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
3.
In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?
4.
Evaluate $frac{n!}{(n-r)!}$, when (ii) $n = 9, r = 5$.
5.
In how many ways can the letters of the word PERMUTATIONS be arranged if the (iii) there are always 4 letters between P and S?
6.
In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions ?
7.
In how many ways can the letters of the word PERMUTATIONS be arranged if the (ii) vowels are all together,
8.
Determine $n$ if (ii) ${}^{2n}C_3 : {}^nC_3 = 11 : 1$
9.
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?
10.
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,
11.
How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?
12.
Evaluate (ii) $4! – 3!$
13.
How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?
14.
Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.
15.
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 ?
16.
How many 4-digit numbers are there with no digit repeated?
17.
Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even?
18.
How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?
19.
From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person can not hold more than one position?
20.
A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.
CBSE - Class 11 Mathematics Permutations and Combinations Worksheet
