Permutations and Combinations (Part - 1)

Introduction:
Permutations and combinations are important concepts in mathematics, particularly in the field of combinatorics. They are used to count and arrange objects in different ways. Permutations refer to the arrangement of objects in a specific order, while combinations refer to the selection of objects without considering the order.

MCQ Test on Permutations and Combinations:
Here is a MCQ test on permutations and combinations for Class XI. Each question will have multiple options, and you need to select the correct one. Let's dive into the questions:

1. Question: In how many ways can the letters of the word "EDUCATION" be arranged?
a) 40320
b) 362880
c) 3628800
d) 720

2. Question: How many 3-digit numbers can be formed using the digits 1, 2, 3, 4, and 5 without repetition?
a) 60
b) 120
c) 240
d) 720

3. Question: In how many ways can 5 different books be arranged on a shelf?
a) 20
b) 60
c) 120
d) 720

4. Question: How many 4-letter words can be formed using the letters of the word "MATHS"?
a) 24
b) 48
c) 120
d) 720

5. Question: In how many ways can a committee of 3 students be formed from a group of 8 students?
a) 24
b) 56
c) 84
d) 336

Explanation:
1. Answer: c) 3628800
The word "EDUCATION" has a total of 10 letters. Therefore, the number of ways to arrange these letters is 10 factorial, denoted as 10!.
10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3628800

2. Answer: b) 120
To form a 3-digit number without repetition using the digits 1, 2, 3, 4, and 5, we have 5 choices for the first digit, 4 choices for the second digit, and 3 choices for the third digit.
Therefore, the total number of ways is 5 * 4 * 3 = 60.

3. Answer: d) 720
The 5 different books can be arranged on the shelf in 5 factorial ways, denoted as 5!.
5! = 5 * 4 * 3 * 2 * 1 = 120

4. Answer: a) 24
The word "MATHS" has a total of 5 letters. Therefore, the number of ways to form a 4-letter word using