Question

2. How many 4 - digit numbers can
be made by using digits 1 to 7
(repetition is not allowed), if the
digit 4 will always be there in the
number?
a. 120 b. 240 c. 480 d. 840​

Answer 1

Answer:

d) 480

Step-by-step explanation:

Place 4 in all the four places one by one and arrange the rest.

4 _ _ _ = 1*6*5*4 = 120

_ 4 _ _ = 6*1*5*4 = 120

_ _ 4 _ = 6*5*1*4 = 120

_ _ _ 4 = 6*5*4*1 = 120

Total = 120*4= 480.

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Answer 2

Step-by-step explanation:

We have to make 4 digit number from 1, 2, 3, 4, 5, 6 and 7, given repetition of any of these numbers is not allowed.

So we have four places to make 4 digit number as

_ _ _ _

For 1st place we have 7 choices.

For 2nd place we have 6 choices as we have already used one number and repetition is not allowed.

For 3rd place we have 5 choices as we have already used two numbers and repetition is not allowed.

For 4th place we have 4 choices as we have already used three numbers and repetition is not allowed.

Therefore, the total number of possible combinations will be

7*6*5*4=840.