Permutation Test

Result

Permutation Test - 1

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Weekly Quiz Competition

Question 1
1 / -0

A college offers 7 courses in the morning and 5 in the evening. The number of ways a student can select exactly one course, either in the morning or in the evening

A
27

B
15

C
12

D
35

Solution

The student has seven choices from the morning courses out of which he can select one course in 7 ways.

For the evening course, he has 5 choices out of which he can select one course in 5 ways.

Hence he has total number of 7 + 5 = 12 choices.
Question 2
1 / -0

In a monthly test, the teacher decides that there will be three questions, one from each of exercise 7, 8 and 9 of the text book. If there are 12 questions in exercise 7, 18 in exercise 8 and 9 in exercise 9, in how many ways can three questions be selected

A
1944

B
1499

C
4991

D
None of these

Solution

There are 12 questions in exercise 7. So, one question from exercise 7 can be selected in 12 ways. Exercise 8 contains 18 questions. So, second question can be selected in 18 ways. There are 9 questions in exercise 9. So, third question can be selected in 9 ways. Hence, three questions can be selected in 12 × 18 × 9 = 1944 ways.
Question 3
1 / -0

How many numbers of five digits can be formed from the numbers 2, 0, 4, 3, 8 when repetition of digit is not allowed

A
96

B
120

C
144

D
14

Solution

Given numbers are 2, 0, 4, 3, 8

Numbers can be formed = {Total – Those beginning with 0}

= {5 ! – 4 !} = 120 – 24 = 96.
Question 4
1 / -0

The number of 5 digit telephone numbers having at least one of their digits repeated is

A
90,000

B
100,000

C
30,240

D
69,760

Solution

Using the digits 0, 1, 2,.......,9 the number of five digit telephone numbers which can be formed is 10⁵. (since repetition is allowed)

The number of five digit telephone numbers which have none of the digits repeated = ¹⁰P₅ = 30240

The required number of telephone numbers = 10⁵ - 30240 = 69760