Permutations and Combinations Test

Result

Permutations and Combinations Test - 7

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Weekly Quiz Competition

Question 1
2 / -0.83

How many chords can be drawn through 10 points on a circle?

A
45

B
20

C
40

D
10!

Solution

For the 1st point chords can be drawn with joining 9 other points.
For the 2nd point distinct chords can be drawn with joining 8 other points.
For the 9th point distinct chords can be drawn with joining 1 other point.
So, total no. of points = 9 + 8 + 7 + . . . . . . + 1 = 45
Question 2
2 / -0.83

In a room there are 2 green chairs, 3 yellow chairs and 4 blue chairs. In how many ways can Raj choose 3 chairs so that at least one yellow chair is included?

A
3

B
30

C
64

D
84

Solution

At least one yellow chair means “total way no yellow chair ”
Total ways to select 3 chair form the total (2+3+4) = ⁹ C₃

Now, we dont want even one yellow chair.
So we should select 3 chairs from 6 chairs (2 green &4 blue) = ⁶ C₃

Hence, ways to select at least one yellow chair = 84 - 20 = 64 ways.
Question 3
2 / -0.83

In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 courses are compulsory for every student.

A
30

B
32

C
34

D
35

Solution
Question 4
2 / -0.83

C(20,r) = C(20, r + 2) What is the value of C(r,6) ?

A
84

B
24

C
48

D
12

Solution

²⁰ C_r = ²⁰ C_r+2
ⁿ C_r = ⁿ C_n-r
=>r + (n −r) = n
⇒r + r + 2 = 20
⇒2r = 18
⇒r = 9
^r C₆ = ⁹ C₆
⇒9!/(6!*3!)
= 84
Question 5
2 / -0.83

A group consists of 4 girls and 7 boys. in how many ways a team of 5 members be selected consisting of 2 girls and 3 boys.

A
120 ways

B
210 ways

C
2! x 3!

D
¹¹ C₅

Solution

Total number of girls in the group = 4
Total number of boys in the group = 7
Probability of selecting atleast three boy and two girl = ⁴ C₂ ×⁷ C₃
= 210
Question 6
2 / -0.83

In how many ways can an examinee choose 5 questions out of 8 in a paper of Physics?

A
42

B
56

C
7!

D
8!

Solution

8C5
= 8!/5!*3!
= 8*7*6*5!/5!*3!
= 56
Question 7
2 / -0.83

How many triangles can be formed by joining four points on a circle?

A
8

B
6

C
4

D
2

Solution

Triangle formed = mC3
Therefore, 4 points on circle, m = 4
4C3 = 4C1
⇒4
Question 8
2 / -0.83

In how many ways can one select a cricket team of eleven from 13 players in which only 5 players can bowl. If each cricket team of 11 must include at least 4 bowlers.

A
28

B
40

C
12

D
68

Solution
Question 9
2 / -0.83

A committee consists of 5 students 3 girls and 2 boys. If the team is to be formed out of 7 boys and 5 girls, then how many ways this selection can be made?

A
C(7,3) ×C(5,2)

B
C(7,5) ×C(3,2)

C
C(7,2) ×C(5,3)

D
C(5,7) ×C(2,3)

Solution

out of 7 persons , we have to select exactly 3 girls . hence, it 's clear that remaining 4 persons will be boys .

Now, number of ways taken 4 boys from 9 boys = 9C4
and number of ways taken 3 girls from 4 girls = 4C3

hence, by fundamental principle of counting ,
total number of ways for making the committee = 9C4 ×4C3
= 9!/5!.4! ×4!/3!
= 9 ×8 ×7 ×6/3 ×2 ×1
= 9 ×8 ×7
= 504 ways
Question 10
2 / -0.83

Find the number of diagonals of an n-sided polygon.

A
n

B
(n-1)

C
n(n-1)/2

D
n(n-3)/2

Solution

For a convex n-sided polygon, there are n vertices, and from each vertex you can draw n-3 diagonals, so the total number of diagonals that can be drawn is n(n-3).The number of diagonals in a polygon = n(n-3)/2, where n is the number of polygon sides.