Question

A four digit number (with no repetitions) is to be formed from the set of numbers {0,1,2,3,4,5,6,7}. Find the probability that the number

a) is even
b) is odd
c) is less than 4000
d) is less than 4000, given that it is greater than 3000

Answer 1

even # --------- if it ends with 0, # of ways = 6*5*4 = 120 if not, 3 ways for ending digit, 5 ways for 1st digit, 5*4 for middle digits = 300
so total ways = 420
odd # --------- 4 ways of ending digit, 5 ways for 1st digit, 5*4 for middle digits = 400 ways
< 4000: ---------- 3 ways for starting digit, 6*5*4 ways for remaining digits = 360 ways
> 3000 & < 4000 ------------------------ 1 way for starting digit , 6*5*4 for remaining digits = 120 ways