Permutation and Combination - Class 11 (HSSC-I) Mathematics

Q1

${}^{7}C_4 + {}^{7}C_3$ is equal to

Q2

$\dfrac{0!(5-1)!}{4}$ is equal to

Q3

$^{8}P_{6}$ is equal to

Q4

In a class of $40$ students, $15$ are to be selected for the art society. There are $3$ particular students who are good in arts and the selectors desire to include them in the society. In how many ways can the society members be selected?

Q5

On evaluating, the combination $\dbinom{ab}{ab}$ reduces to

Q6

In a garden, five chairs are placed in a row. The expression to find the number of ways these chairs can be filled by five persons, when two persons always sit next to each other, is

Q7

The value of $1! - \left[0! \times \dfrac{n!}{(n-1)!}\right]$ is equal to

Q8

Solve the following question:

Q9

A school is selecting $3$ students from a group of $10$ to represent the school in a debate competition. The number of ways through which the students can be selected is

Q10

$\dfrac{0!\,(5-1)!}{4}$ is equal to

Q11

A man goes to a bakery where he finds Samosas ($S$), Vegetable rolls ($R$) and Potato Cutlets ($P$). They are served with Chatni ($C$) or Ketchup ($K$). Which tree diagram illustrates the given situation for all the possible combinations?

Q12

The possible number of arrangements of the letters of the word SYSTEMATIC, taken all at a time, is equal to