Question

4. Assume that the repetition is not allowed. How many orders that can be build from 6 numbers, 2, 3, 4, 5, 7 and 9, taken 3 at a time, to produce any number in hundreds,

a) Without any condition

b) Produce values less than 400.

c) Produce the even values.

d) Produce the odd values.

e) Produce values that are the multiple of 5.

Answer 1

a)

Since repetition is not allowed so first digit can be selected in 6 ways,second in 5 ways and third is 4 ways.

So possible number of numbers in hundreds is

6*5*4=120

b)

Produce value will be less than 400 if digit at hundred place is either 2 and 3 so digit at hundred place can be filled in 2 ways, rest two digits can be fileed in 5 and 4 ways respectively so

2 * 5* 4 = 40

c)

For even number, digit at unit place must be either 2 or 4.

So digit at unit place can be filled in 2 ways, rest two digits can be fileed in 5 and 4 ways respectively so

2 * 5* 4 = 40

d)

For odd number, digit at unit place must be either 3, 5, 7 or 9.

So digit at unit place can be filled in 4 ways, rest two digits can be fileed in 5 and 4 ways respectively so

4 * 5* 4 = 80

e)

For multiple of 5, digit at unit place must be 5.

So digit at unit place can be filled in 1 way, rest two digits can be fileed in 5 and 4 ways respectively so

1 * 5* 4 = 20