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?
The number of arrangements in which Veena can visit the 4 cities A, B, C, D
=
The sample space of the 24 arrangements is:
S = n(S) = 24
(i) Event E: She visits A before B. E = {ABCD, ABDC, ACBD, ACDB, ADBC, ADCB, CABD, CADB, CDAB, DABC, DACB, DCAB}
n(E) = 12
Hence,
(ii) Event F: Veena visits A before B and B before C. F = {ABCD, ABDC, ADBC, DABC}
n(F) = 4
Hence,
(iii) Event G: Veena Visits A first and B last G = {ACDB, ADCB}
n(G) = 2
Hence,
(iv) Event H: Veena visits A either first or second. H = {ABCD, ABDC, ACBD, ACDB, ADBC, ADCB, BACD, BADC, CABD, CADB, DACB, DABC}
n(H) = 12
Hence,
(v) Event k: Veena visits A just before B. K = {ABCD, ABDC, CABD, CDAB, DABC, DCAB}
n(K) = 6
Hence,
In a relay race, there are five teams, A, B, C, D and E.
What is the porbability
(i) that A, B, C finish first, second and third respectively?
(ii) 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.