# Permutation and Combination Questions Answers

• #### 1. Evaluate \begin{aligned} \frac{30!}{28!} \end{aligned}

1. 970
2. 870
3. 770
4. 670

Explanation:

\begin{aligned}
= \frac{30!}{28!} \\
= \frac{30 * 29 * 28!}{28!} \\
= 30 * 29 = 870
\end{aligned}

• #### 2. Evaluate permutation equation \begin{aligned} ^{59}{P}_3 \end{aligned}

1. 195052
2. 195053
3. 195054
4. 185054

Explanation:

\begin{aligned}
^n{P}_r = \frac{n!}{(n-r)!} \\
^{59}{P}_3 = \frac{59!}{(56)!} \\
= \frac{59 * 58 * 57 * 56!}{(56)!} \\
= 195054
\end{aligned}

• #### 3. Evaluate permutation \begin{aligned} ^5{P}_5 \end{aligned}

1. 120
2. 110
3. 98
4. 24

Explanation:

\begin{aligned}
^n{P}_n = n! \\
^5{P}_5 = 5*4*3*2*1 \\
= 120

\end{aligned}

• #### 4. Evaluate permutation equation \begin{aligned} ^{75}{P}_2\end{aligned}

1. 5200
2. 5300
3. 5450
4. 5550

Explanation:

\begin{aligned}
^n{P}_r = \frac{n!}{(n-r)!} \\
^{75}{P}_2 = \frac{75!}{(75-2)!} \\
= \frac{75*74*73!}{(73)!} \\
= 5550

\end{aligned}

• #### 5. Evaluate combination \begin{aligned} ^{100}{C}_{97} = \frac{100!}{(97)!(3)!} \\ \end{aligned}

1. 161700
2. 151700
3. 141700
4. 131700

Explanation:

\begin{aligned}
^{n}{C}_r = \frac{n!}{(r)!(n-r)!} \\
^{100}{C}_{97} = \frac{100!}{(97)!(3)!} \\
= \frac{100*99*98*97!}{(97)!(3)!} \\
= \frac{100*99*98}{3*2*1} \\
= \frac{100*99*98}{3*2*1} \\
= 161700
\end{aligned}

• #### 6. Evaluate combination \begin{aligned} ^{100}{C}_{100} \end{aligned}

1. 10000
2. 1000
3. 10
4. 1

Explanation:

\begin{aligned}
^{n}{C}_{n} = 1 \\
^{100}{C}_{100} = 1
\end{aligned}

• #### 7. How many words can be formed by using all letters of TIHAR

1. 100
2. 120
3. 140
4. 160

Explanation:

First thing to understand in this question is that it is a permutation question.
Total number of words = 5
Required number =
\begin{aligned}
^5{P}_5 = 5! \\
= 5*4*3*2*1 = 120
\end{aligned}

• #### innovative 5 years ago

yaar thode toh hard questions rakho....
All boring questions.
Not impressed by the level of questions.!!!!!!!!!!!!

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• #### ochieng isaac 7 years ago

examples of permutation