On her vacations, Veena visits four cities (A, B, C and D) in a random order. What is the probability that she visits:
(i) A before B? (ii) A before B and B before C?
(iii) A first and B last? (iv) A either first or second (v) A just before B?Â
In a relay race, there are five teams, A, B, C, D and E.
What is the porbability
(i)Â that A, B, C finish first, second and third respectively?
(ii)Â that A, B and C are first three to finish (in any order)?
Letters of the word ‘EDUCATION’ are re-arranged. Find the probability that the vowels are always together.
Also, find the probability that the vowels are not all together.
Number of letters in the word ' EDUCATION' = 9
 Number of vowels = 5
Number of consonants = 4
Number of arrangements for 9 letters = 9!           n(S) = 9!
Event A: The vowels are always together            n(A) = r! (n - r + 1)!
where r = 5, n - r + 1 = 9 - 5 + 1 = 5Â Â Â Â Â Â Â Â Â Â Â Â n(A) =Â
Hence, Â Â Â Â
Also, the probability that not all the vowels are together
        Â