Combinatorics

[q_fruit]

These are probably quite easy...just not to me.

Q1a: How many different 3 digit numbers can be formed using the digits 1,3, 5, 7 and 9 if the digits may be repeated?

The answer is 5 x 5 x 5 = 125

- i understand this but -->


Q1b: If they cannot be repeated?
The answer is 5 x 4 x 3 = 60

-i can't picture in my mind why you go 5 x 4 x 3. help plz?

My second question is...

Q2: In a 7 horse race, Bill thinks horses 1, 4, and 6 will be the top 3 horses, but not necessarily in that horder. If BIll is correct, how many different outcomes are possible?

The answer is 3 x 2 x 1 x 4 x 3 x 2 x 1 = 144
- why??

 

[Gene]

Any one of the five numbers can be in the first position. After the first is filled in there four possible numbers for the second position. There are 5*4 two digit numbers. The third can be any of the three remaining digits. 20*3 = 60 three digit numbers.

Same reasoning for the first three positions. 3*2*1. Fourth position any of the 4 remaining horses. Fifth any of 3. Sixth etiher of 2. Seventh is the only one left. 4*3*2*1. Since they are independent (Any of the 6 first three possibilities with any of the 24 also ran possibilities.) you multiply them.