Permutations and Combinations Test

Result

Permutations and Combinations Test - 8

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Weekly Quiz Competition

Question 1
2 / -0.83

The number of ways in which three different rings can be worn in four fingers with at most one in each finger, are

A
12

B
64

C
24

D
6

Solution

The total number of ways is same as the number of arrangements of 4 fingers, taken 3 at a time.
So, required number of ways = ⁴ P₃
= 4!/(4-3)!
= 4!/1!
= 4! =>24
Question 2
2 / -0.83

A room has 8 doors. In how many ways, a man can enter in the room through one door and exit through a different door?

A
5040

B
40320

C
56

D
8

Solution

The person has 8 options to enter the hall. For each of these 8 options, he has 7 options to exit the hall. Thus, he has 8 ×7 = 56 ways to enter and exit from different doors.
Question 3
2 / -0.83

The total number of ways of answering 5 objective questions, each question having four choices are

A
2880

B
120

C
1024

D
None of the above

Solution

There are five questions
Each question has 4 options
No. of possible ways of answering each question is four
No. of Possible ways for Q1 = 4
No. of Possible ways for Q2 = 4
No. of Possible ways for Q3 = 4
No. of Possible ways for Q4 = 4
No. of Possible ways for Q5 = 4
So, Total number of ways of answering 5 objective type questions, each question having 4 choices = 4⁵
= 1024
Question 4
2 / -0.83

In how many ways, a party of 5 men and 5 women be seated at a circular table, so that no two women are adjacent?

A
720

B
14400

C
2880

D
1440

Solution

Lets first place the men (M). '*'here indicates the linker of round table

* M -M - M - M - M *
which is in (5-1)! ways
So we have to place the women in between the men which is on the 5 empty seats ( 4 -'s and 1 linker i.e * )
So 5 women can sit on 5 seats in (5)! ways or
1st seat in 5 ways
2nd seat 4
3rd seat 3
4th seat 2
5th seat 1
i.e 5*4*3*2*1 ways
So the answer is 5! * 4! = 2880
Question 5
2 / -0.83

The measure of an interior angle of a regular polygon is 140 °. The number of sides and diagonals in this polygon are:

A
8,20

B
7,17

C
7,14

D
9,27

Solution

Since the exterior angle 140 degrees, The sum of the interior angles = (2n - 4)* right angles. So 140n = (2n - 4)* right angles, or
140n = (2n - 4)*90, or
140n = 180n - 360o, or
40n = 360 °, or
n = 9 sides.
Question 6
2 / -0.83

In how many ways can a cricket team of 11 players be chosen out from a squad of 14 players, if 5 particular players are always chosen?

A
84

B
144

C
1001

D
1365

Solution

Total no of players = 14 out of which 5 are fixed.
So, 11-5 = 6
Remaining players = 14 - 6
= 9 players
9C6 = 9!/(3!*6!)
= 84
Question 7
2 / -0.83

A team of 7 players is to be formed out of 5 under 19 players and 6 senior players. In how many ways, the team can be chosen when at least 4 senior players are included?

A
185

B
215

C
115

D
125

Solution

No. of ways to select 4 senior and 3 U-19 players = ⁶ C₄ * ⁵ C3 = 150
No. of ways to select 5 senior and 2 U-19 players = ⁶ C₅ * ⁵ C2 = 60
No. of ways to select 6 senior and 1 U-19 players = ⁶ C₆ * ⁵ C1 = 5
Total no. of ways to select the team = 150 + 60 + 5 = 215
Question 8
2 / -0.83

Four alphabets A, M, P, O are purchased from a warehouse. How many ordered pairs of initials can be formed using these?

A
10

B
16

C
18

D
12

Solution

Total number of letters = 4
Number of ordered pairs of letters that can be formed like (A, M) or (P, O) etc = ⁴ P₂ = 4!/2!
= 24/2
= 12
Question 9
2 / -0.83

How many words beginning with ‘T ’and ending with ‘E ’can be formed using the letters of the word ”TRIANGLE ”?

A
625

B
720

C
24

D
120

Solution

There are 8 letters in the word TRIANGLE.
2 alphabets are fixed, remaining are 6 alphabets
So, number of arrangements = ⁶ P₆
= 6!
= 720
Question 10
2 / -0.83

In how many ways can 4 red, 3 yellow and 2 green chairs be arranged in a row if the chairs of the same colour are indistinguishable?

A
15120

B
1260

C
362880

D
None of the above

Solution

Total no of balls = 9
red balls = 4
yellow balls = 3
green balls = 2
Total no. of arrangements = 9!/(4!*3!*2!)
= 1260

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Re-Attempt Weekly Quiz Competition

Permutations and Combinations Test - 8

Result

Permutations and Combinations Test - 8

Score

-

Rank

-

SHARING IS CARING

Question 1

12

64

24

6

Solution

Question 2

5040

40320

56

8

Solution

Question 3

2880

120

1024

None of the above

Solution

Question 4

720

14400

2880

1440

Solution

Question 5

8,20

7,17

7,14

9,27

Solution

Question 6

84

144

1001

1365

Solution

Question 7

185

215

115

125

Solution

Question 8

10

16

18

12

Solution

Question 9

625

720

24

120

Solution

Question 10

15120

1260

362880

None of the above

Solution

User

Question Analysis

My Perfomance

Score

-

Rank

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