Telephone Number Permutations

Question

Using the fundamental principle of counting or permutations how many 7 digit telephone numbers are possible if the first digit cannot be 0 and

A. only odd digits may be used.

B. the telephone number must be a multiple of 10(that is, it must end in 0)?

C. the telephone number must be a multiple of 100?

D. the first 3 digits are 481?

E. No repetitions are allowed?

 

This is what I got..

A. 5^7 = 78,125

B. 9 x 10^5 = 9000,000

C 9 x 10^4 = 90,000

D. 10 x 10 x 10 = 1,000

E. 9 x 9 x 8 x  7 x 6 x 5 x 4 = 544,320

 

Just trying to see if I got them correct or not. Thanks!

Answer 1

A, B, C, and E are correct.  

 

D - You are just missing one more digit: 10⁴, not 10³