Question Detail

A box contains 4 red, 3 white and 2 blue balls. Three balls are drawn at random. Find out the number of ways of selecting the balls of different colours

Answer: Option B

Explanation:

This question seems to be a bit typical, isn't, but it is simplest.
1 red ball can be selected in 4C1 ways
1 white ball can be selected in 3C1 ways
1 blue ball can be selected in 2C1 ways

Total number of ways
= 4C1 x 3C1 x 2C1
= 4 x 3 x 2
= 24

Please note that we have multiplied the combination results, we use to add when their is OR condition, and we use to multiply when there is AND condition, In this question it is AND as
1 red AND 1 White AND 1 Blue, so we multiplied.

1. 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}

2. 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}

3. How many words can be formed from the letters of the word "SIGNATURE" so that vowels always come together.

17280
4320
720
80

Answer: Option A

Explanation:

word SIGNATURE contains total 9 letters.
There are four vowels in this word, I, A, U and E

Make it as, SGNTR(IAUE), consider all vowels as 1 letter for now
So total letter are 6.
6 letters can be arranged in 6! ways = 720 ways
Vowels can be arranged in themselves in 4! ways = 24 ways

Required number of ways = 720*24 = 17280

4. Evaluate permutation equation
\begin{aligned} ^{59}{P}_3 \end{aligned}

195052
195053
195054
185054

Answer: Option C

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}

5. In how many ways can the letters of the CHEATER be arranged

20160
2520
360
80

Answer: Option B

Explanation:

As we can see the letter "E" is twice in given word, so Required Number
\begin{aligned}
= \frac{7!}{2!} \\
= \frac{7*6*5*4*3*2!}{2!} \\
= 2520
\end{aligned}

Question Detail

A box contains 4 red, 3 white and 2 blue balls. Three balls are drawn at random. Find out the number of ways of selecting the balls of different colours

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

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

3. How many words can be formed from the letters of the word "SIGNATURE" so that vowels always come together.

4. Evaluate permutation equation \begin{aligned} ^{59}{P}_3 \end{aligned}

5. In how many ways can the letters of the CHEATER be arranged

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

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

4. Evaluate permutation equation
\begin{aligned} ^{59}{P}_3 \end{aligned}