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Class Discussion: Modern Maths
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CAT 2025 Lesson : Class Discussion: Modern Maths - Permutations & Combinations: 1 to 8

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Class Discussion – Permutation & Combinations

Question 1

A class has 8 girls and 6 boys. In how many different ways can the 4 positions of Head Girl, Head Boy, Dy. Head Girl and Dy. Head Boy be filled from the 14 students in the class?

Answer:

Question 2

Using only the digits 0, 3, 4, 5 and 6, how many positive integers less than 500,000 can be formed (repetition of digits is allowed)?

Answer:

Question 3

How many 4-digit positive integers can be formed using the digits 5, 6, 7, 8, 9 and 0 such that no 2 digits are repeated and the integers are perfectly divisible by 4?

Answer:

Question 4

If a project team needs to be formed by selecting one or more people from 6 programmers, 4 designers and 3 testers, such that the team has at least 1 person of each kind, then in how many different ways can the team be formed?

Answer:

Question 5

Vivekh took an aptitude test containing 20 questions. Each of these questions had 4 options each. He got 3 marks for every correct answer. For an incorrect attempt, 1 mark was deducted and no marks were given or deducted for questions he did not attempt.

In how many different ways could he have answered 1 or more questions in the paper?

4204^{20}
420−14^{20} - 1
5205^{20}
520−15^{20} - 1

Question 6

Vivekh took an aptitude test containing 20 questions. Each of these questions had 4 options each. He got 3 marks for every correct answer. For an incorrect attempt, 1 mark was deducted and no marks were given or deducted for questions he did not attempt.

In how many different ways could he have answered 3 or more questions in the paper?

20C17×517^{20}\text{C}_{17} \times 5^{17}
20C17×417^{20}\text{C}_{17} \times 4^{17}
520−[1+(20C1×4)+(20C2×42)]5^{20} - [ 1 + (^{20}\text{C}_{1} \times 4) + (^{20}\text{C}_{2} \times 4^{2})]
520−1−(20C1×5)−(20C2×52)5^{20} - 1 - (^{20}\text{C}_{1} \times 5) - (^{20}\text{C}_{2} \times 5^{2})

Question 7

Vivekh took an aptitude test containing 20 questions. Each of these questions had 4 options each. He got 3 marks for every correct answer. For an incorrect attempt, 1 mark was deducted and no marks were given or deducted for questions he did not attempt.

In how many ways could he have attempted all the questions and have scored 44 marks

20C16×416^{20}\text{C}_{16} \times 4^{16}
20C16×34^{20}\text{C}_{16} \times 3^{4}
20C4×44^{20}\text{C}_{4} \times 4^{4}
20C4×316^{20}\text{C}_{4} \times 3^{16}

Question 8

Vivekh took an aptitude test containing 20 questions. Each of these questions had 4 options each. He got 3 marks for every correct answer. For an incorrect attempt, 1 mark was deducted and no marks were given or deducted for questions he did not attempt.

In how many ways could he have got exactly 12 questions correct?

20C8×48^{20}\text{C}_{8} \times 4^{8}
20C12×38^{20}\text{C}_{12} \times 3^{8}
20C12×312^{20}\text{C}_{12} \times 3^{12}
20C8×412^{20}\text{C}_{8} \times 4^{12}

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