If the letters of the word HORIZON be arranged at random, what is the probability that all the vowels are together?
S = 7!/2! = (7 × 6 × 5 × 4 × 3 × 2 × 1 )/(2 × 1)= 2520 Let E= event of getting all vowels are together n(E) = (5!x3! )/2! = 360 ∴ P (E) = (n(E))/(n(S)) = 360/2520 = 1/7
In which of the following expressions does the expression ‘L > B’ and ‘R < N’ is true?
Statements: X ≥ W > O = F ≥ B ≥ J; M < A ≤ J
Conclusions:
I. M < B
II. O ≥ A
III. O < A
...14. Statement: L ≥ X ≤ Z > Y ≤ A, Y = B ≥ CÂ
Conclusion: I. C > A                         II. A ≥ C
...Statements: J ≥ K ≥ A = M, K ≥ O > W ≥ X
Conclusion:
I. J ≥ X
II. J > X
Statement: L ≥ M ≤ R = S; M > N ≥ P
Conclusions:
I. P ≤ M
II. L > N
Statements: F @ R, R $ J, V % J, V # Z
Conclusions: I. F * VÂ Â Â Â Â Â Â II. R * VÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â...
Statements: A ≥ B ≥ Y = Z = M ≥ N ≤ E ≤ F = J
Conclusions:
I. F > Z
II. J ≤ Y
Statements: D < O = Q > U < I ≤ R; K ≥ O = I; R > H ≥ G
Conclusions:
I. R > O
II. K > U
III. H ≥ Q
Statement: H > G = M > S ; GÂ `>=` Â T > L; MÂ `<=` Â F <Â U
    Conclusion:  I. L > M          II. G < U
...Statements: B & Y, Y # M, M $ X, X @ S
Conclusions: I. X $ YÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â II. X & Y
...