Permutation and Combination Questions Answers

1. Evaluate \begin{aligned}
\frac{30!}{28!}
\end{aligned} 970
 870
 770
 670
Answer And Explanation
Answer: Option B
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} 195052
 195053
 195054
 185054
Answer And Explanation
Answer: Option C
Explanation:
\begin{aligned}
^n{P}_r = \frac{n!}{(nr)!} \\
^{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} 120
 110
 98
 24
Answer And Explanation
Answer: Option A
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} 5200
 5300
 5450
 5550
Answer And Explanation
Answer: Option D
Explanation:
\begin{aligned}
^n{P}_r = \frac{n!}{(nr)!} \\
^{75}{P}_2 = \frac{75!}{(752)!} \\
= \frac{75*74*73!}{(73)!} \\
= 5550
\end{aligned} 
5. Evaluate combination
\begin{aligned}
^{100}{C}_{97} = \frac{100!}{(97)!(3)!} \\
\end{aligned} 161700
 151700
 141700
 131700
Answer And Explanation
Answer: Option A
Explanation:
\begin{aligned}
^{n}{C}_r = \frac{n!}{(r)!(nr)!} \\
^{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} 10000
 1000
 10
 1
Answer And Explanation
Answer: Option D
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
 100
 120
 140
 160
Answer And Explanation
Answer: Option B
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 3 years ago
yaar thode toh hard questions rakho....
All boring questions.
Not impressed by the level of questions.!!!!!!!!!!!! 
Kannhaa..... 3 years ago
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ochieng isaac 4 years ago
examples of permutation