Questions covered in Basic

Review the question prompts below before starting the timed test. Try each problem independently, then use the interactive test to record your answers and review the worked solutions.

1. The value of $0! + 1!$ is
2. If $^nP_2 = 20$, then $n$ is
3. The number of ways 5 people can sit in a row is
4. $^nC_r + ^nC_{r-1}$ is equal to
5. How many 2-digit numbers can be formed using the digits 1, 2, 3, 4 without repetition?
6. Compute $\frac{8!}{6! \times 2!}$.
7. If $^nC_9 = ^nC_8$, find $^nC_{17}$.
8. How many 3-digit numbers can be formed from the digits 1, 2, 3, 4, 5 if repetition of digits is allowed?
9. Find $n$ if $^{2n}C_3 : ^nC_3 = 11 : 1$.
10. A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of these committees would consist of 1 man and 2 women?
11. Find the number of different 8-letter arrangements that can be made from the letters of the word DAUGHTER so that:
    (i) all vowels occur together.
    (ii) all vowels do not occur together.
12. Case Study: A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has:
    (i) no girl?
    (ii) at least one boy and one girl?
    (iii) at least 3 girls?