Question

Three Digits from {1,2,3,4,5,6,7} are chosen and arranged in a row without replacement.

1. Determine the number of different outcomes we could obtain
2. Find the probability of each event:
   1. The digit 1 appears
   2. All digits are even
   3. At least one digit is even
   4. The number is divisible by 5

Answer 1

a) total number of outcomes =N(Select 3 from 7 and arrange )=⁷P₃ =7!/4! =210

b)

a) P(digit 1 appears) =P(selecting other 2 from remaining 6)= ⁶C₂/⁷C₃ =15/35 =3/7

b)P(all are even) =P(Select 3 dgits from 3 even) =³C₃/⁷C₃ =1/35

c)P(at least one is even) =1-P(all are odd) =1-P(select 3 from 4 odd numbers)=1-⁴C₃/⁷C₃ =1-4/35 =31/35

d)P(number is divisible by 5) =P(last digit is 5) =1/7