how many three digit numbers can be made with the digits 1,2,3,4,5,6 and 7 if a) repetitions are allowed b) no digits is to be repeated in a number?

Question

how many three digit numbers can be made with the digits 1,2,3,4,5,6 and 7 if a) repetitions are allowed b) no digits is to be repeated in a number?

Answer 1

Hi Thea

 

With 7 numbers, we can create three digit numbers like this.

 

a)  With repetitions would suggest with replacement.

We'd have 7 options for the first digit, 7 options for the 2nd digit and 7 choices for the 3rd digit

7³ = 343 combinations

 

b) Without repeated numbers, would suggest without replacement

We'd have 7 options for the first digit, 6 options for the 2nd digit and 5 choices for the 3rd digit

7•6•5 = 210 combinations