How many different numbers can be formed fro the set of seven numbers (1,2,3,4,5,6,7) if

Question

a) repitition is allowed
b) repitition is not allowed
c) repitition is allowed and the tird digit must be different from the second digit?

Answer 1

a) digits can repeat
number of cases = single digits + double digits + .. + 7digit numbers
= 7 + 7^2 + 7^3 + ... + 7^7
a geometric series, with a = 7, r = 7 , n = 7
sum = 7(7^7 - 1)/(7-1) = 960799

b) repeats are not allowed
single digits --- 7
double digits, choices = C(7,2) = 21 , arranged in 2! ways = 42
triple digits --- C(7,3) x 3! = 210
4 digits ------- C(7,4) x 4! = 840
5 digits ------- C(7,5) x 5! = 2520
6 digits -------- C(7,6) x 6! = 5040
7 digits --------- 7! = 5040
add them up , notice the above number are just like using P(n,r)

c) can only apply to 3 digit or more numbers.
Let me know your thinking on this.

Answer 2

sorry its supposed to be how many different five digit numbers! can be formed from the seven. sorry!!!!

Answer 3

That makes the whole question much easier!
So what do you think?

Answer 4

for a i had
7 x 7 x 7 x 7 x 7
= 16, 807

for b i had
7 x 6 x 5 x 4 x 3
= 2520

for c i had
7 x 7 x 6 x 7 x 7

c i am very unsure of though.