In the below word how many words are there in whic | Permutations and Combinations Questions & Answers

Q:

How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9 which are divisible by 5 and none of the digits is repeated ?

A) 15	B) 20
C) 5	D) 10

Answer & Explanation Answer: B) 20

Explanation:

Since each number to be divisible by 5, we must have 5 0r 0 at the units place. But in given digits we have only 5.

So, there is one way of doing it.

Tens place can be filled by any of the remaining 5 numbers.So, there are 5 ways of filling the tens place.

The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.

Required number of numbers = (1 x 5 x 4) = 20.

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12 7902

Q:

In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there ?

A) 205	B) 194
C) 209	D) 159

Answer & Explanation Answer: C) 209

Explanation:

We may have (1 boy and 3 girls)or(2boys and 2 girls)or(3 boys and 1 girl)or(4 boys).

Required number of ways = ( ${}^{6}C_{1} \times {}^{4}C_{3}$ ) + $({}^{6}C_{2} \times {}^{4}C_{2})$ + ( ${}^{6}C_{3} \times {}^{4}C_{1}$ ) + ( ${}^{6}C_{4}$ )

= (24+90+80+15)

= 209.

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7 3530

Q:

In a bag, there are 8 red, 7 blue and 6 green flowers. One of the flower is picked up randomly. What is the probability that it is neither red nor green ?

$A) \frac{1}{3}$

$B) \frac{8}{21}$

$C) \frac{6}{21}$

$D) \frac{20}{21}$

A) Option A	B) Option B
C) Option C	D) Option D

Answer & Explanation Answer: A) Option A

Explanation:

Total number of flowers = (8+7+6) = 21.

Let E = event that the flower drawn is neither red nor green.

= event taht the flower drawn is blue.

--> n(E)= 7

--> P(E)= $\frac{7}{21}$ = $\frac{1}{3}$

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8 3123

Q:

A box contains 5 green, 4 yellow and 5 white pearls. Four pearls are drawn at random. What is the probability that they are not of the same colour ?

A) 11/91

B) 4/11

C) 1/11

D) 90/91

A) Option A	B) Option B
C) Option C	D) Option D

Answer & Explanation Answer: D) Option D

Explanation:

Let S be the sample space. Then,
n(s) = number of ways of drawing 4 pearls out of 14

= $C_{4}^{14}$ ways = $\frac{14 \times 13 \times 12 \times 11}{4 \times 3 \times 2 \times 1}$ = 1001

Let E be the event of drawing 4 pearls of the same colour.
Then, E = event of drawing (4 pearls out of 5) or (4 pearls out of 4) or (4 pearls out of 5)

$\Rightarrow C_{1}^{5} + C_{4}^{4} + C_{1}^{5}$ = 5+1+5 =11

P(E) = $\frac{n (E)}{n (S)} = \frac{11}{1001} = \frac{1}{91}$

Required probability = $1 - \frac{1}{91} = \frac{90}{91}$

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8 4595

Q:

Four ladies A, B, C and D and four gentlemen E, F, G and H are sitting in a circle round a table facing each other.

Directions:

(1) No two ladies or two gentlemen are sitting side by side.

(2) C, who is sitting between G and E is facing D.

(3) F is between D and A and is facing G.

(4) H is to the right of B.

Question:

1. Who are immediate neighbours of B?

2. E is facing whom?

A) G & H , H	B) F & H , B
C) E & F , F	D) E & H , G

Answer & Explanation Answer: A) G & H , H

Explanation:

From the directions given :

f11482726547.png image

From the fig. it is clear that

1) neighbours of B are G , H.

2) E is facing H.

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22 20338

Q:

From a bunch of flowers having 16 red roses and 14 white roses, four flowers have to be selected. In how many different ways can they be selected such that at least one red rose is selected?

A) 27405	B) 26584
C) 26585	D) 27404

Answer & Explanation Answer: D) 27404

Explanation:

Given total 16 Red roses and 14 White roses = 30 roses

Four flowers have to be selected from 30 i.e, $C_{4}^{30}$ = 27405 Ways

Now, atleast one Red rose is selected i.e, 27405(total) - 1(all four are white roses) = 27404 ways.

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10 7424

Q:

A group consists of 4 couples in which each of the 4 boys have one girl friend.In how many ways they can be arranged in a straight line such that boys and girls occupies alternate positions?

Answer

Answer : 1152

Total positions are 8.

In that boys can be arranged in 4 places and girls can be arranged in 4 places and hence this can be done in 2 ways.

i.e => 4! x 4! x 2 = 24 x 24 x 2=1152.

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10 2566

Q:

Using numbers from 0 to 9 the number of 5 digit telephone numbers that can be formed is

A) 1,00,000	B) 59,049
C) 3439	D) 6561

Answer & Explanation Answer: C) 3439

Explanation:

The numbers 0,1,2,3,4,5,6,7,8,9 are 10 in number while preparing telephone numbers any number can be used any number of times.

This can be done in $10^{5}$ ways, but '0' is there

So, the numbers starting with '0' are to be excluded is $9^{4}$ numbers.

Total 5 digit telephone numbers = $10^{5} - 9^{4}$ = 3439

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5 3596

A) 120	B) 180
C) 210	D) 240

In the below word how many words are there in which R and W are at the end positions?

RAINBOW

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In the below word how many words are there in which R and W are at the end positions? RAINBOW

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In the below word how many words are there in which R and W are at the end positions?

RAINBOW