suppose you have a bike lock with a code that is seven alpha

suppose you have a bike lock with a code that is seven alphanumeric characters long. The first three of these are letters, and the remaining 4 of these are numbers.

1) Assume that you cannot repeat any letter or number. what is the probability that the letters is in the combination are A, B and C in any order?

2) Assume that you cannot repeat any letter or number. what is the probability that all the numbers are odd?

3Assume that you cannot repeat any letter or number.What is the probability that a combination uses only vowels ( that is A,E, I, O or U) or only even numbers?

Please show the work!

Solution

1) First 3 are letters and remaining 4 are numbers

1) prob for a,b,c to be in letters in any order = 3C3/26C3

= 6/26(25)(24) = 3.846x10^-4

----------------------------------------------------------------------

2) Number are odd means 4 selected out of 5 odd numbers

Hence prob =5C4/10C4 = 2/9

-----------------------------

3) P(Only vowels or even numbers)

= P(only vowels)+P(only even numbers)-P(vowels and even numbers)

= 5C3/26C3+5C4/10C4- (5C3/26C3)(5C4/10C4)

=10/2600 + 5/210-50/2600(210)

= 0.003846+0.02381-0.00009516

=0.02756