Question Detail

Evaluate combination
\begin{aligned}
^{100}{C}_{100}
\end{aligned}

10000
1000
10
1

Answer: Option D

Explanation:

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

1. Evaluate permutation
\begin{aligned}
^5{P}_5
\end{aligned}

Answer: Option A

Explanation:

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

\end{aligned}

2. In how many ways can the letters of the word "CORPORATION" be arranged so that vowels always come together.

5760
50400
2880
None of above

Answer: Option B

Explanation:

Vowels in the word "CORPORATION" are O,O,A,I,O
Lets make it as CRPRTN(OOAIO)

This has 7 lettes, where R is twice so value = 7!/2!
= 2520

Vowel O is 3 times, so vowels can be arranged = 5!/3!

= 20

Total number of words = 2520 * 20 = 50400

3. Evaluate combination
\begin{aligned}
^{100}{C}_{100}
\end{aligned}

10000
1000
10
1

Answer: Option D

Explanation:

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

4. Evaluate \begin{aligned}
\frac{30!}{28!}
\end{aligned}

Answer: Option B

Explanation:

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

5. In how many way the letter of the word "APPLE" can be arranged

Answer: Option C

Explanation:

Friends the main point to note in this question is letter "P" is written twice in the word.
Easy way to solve this type of permutation question is as,

So word APPLE contains 1A, 2P, 1L and 1E
Required number =
\begin{aligned}
= \frac{5!}{1!*2!*1!*1!} \\
= \frac{5*4*3*2!}{2!} \\
= 60
\end{aligned}