Introduction to Combination

Q. A student has to answer any $6$ questions out of $10$ questions came in the question paper. How many number of combinations of question are possible?

1. $\frac{10!}{6!}$
2. $\frac{10!}{4!}$
3. $\frac{10!}{4!6!}$
4. $\frac{10!}{6!6!}$

Q. Which of the following are example(s) of combination?

1. Arrangement of $5$ chocolates taken $3$ at a time.
2. Permutation of $11$ different things without repetition.
3. Selection of $6$ officers out of $13$ officers for post of major general of army.
4. All of the above.

Q. What does the word "Combination" represent?

1. Permutation
2. Probability
3. Counting
4. Selection

Q. There are 10 teachers and 20 students out of which selection of $5$ students are made for a sports committee. Find the number of ways in which this selection can be done.

1. $\frac{10!}{5!.5!}$
2. $\frac{20!}{15!.5!}$
3. $\frac{20!}{10!.5!}$
4. None of the above

Q. How many selections of $3$ letters can be made out of letters of word $\text{EMCOT}$?

1. $20$
2. $60$
3. $10$
4. $30$

Q. What are the different combinations of $2$ digits possible out of $6$ digits $1,2,3,4,5,6$?

1. $6$
2. $15$
3. $24$
4. $12$

Q.

In how many ways can you answer 3 multiple choice questions, with the choices A, B, C and D ?

1. 3
2. 4
3. 64
4. 12