Permutation and Combination Important questions

Q1. From a team of 6 students, in how many ways can we choose a captain and vice-captain assuming one person can not hold more than one position?

Ans: 30

Q2. It is needed to seat 5 boys and 4 girls in a row so that the girl gets the even places. How many arrangements are possible?

Ans: 2880

Q3. Find the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.

Ans: 778320 

Q4. Find the number of 6 digit numbers that can be formed by using the digits 0, 1, 3, 5, 7, and 9. These digits shall be divisible by 10, and no digit shall be repeated?

Ans: 120

Q5. A candidate is required to answer 7 questions out of 12 questions, which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. Find the number of different ways of doing questions.

Ans: 780

Q6. Determine the three-digit numbers that may be formed from the given numbers: 1, 2, 3, 4, and 5, assuming that the numbers can be repeated.

Ans: 125

Q7. You need to assemble a committee of 5 gentlemen and 6 women but there are 8 men and 10 women. Find out different ways in which a committee can be formed.

Ans: 11760

Q8. Out of 18 points in a plane, no three are in the same line except five points which are collinear. Find the number of lines that can be formed joining the point.

Ans: 144