Question
In how many distinct ways can the letters of the word
"MANAGEMENT" be arranged so that all the vowels are always together? (Assume identical letters are indistinguishable.)Solution
ATQ, Word: M A N A G E M E N T Counts: A(2), E(2), M(2), N(2), G(1), T(1). Vowels: A, A, E, E (4 letters, with 2 A’s and 2 E’s). Treat them as one block [V]. Consonants: M, M, N, N, G, T (6 letters). Total items to arrange = 6 consonants + 1 vowel-block = 7 items: [V], M, M, N, N, G, T. Step 1: Arrange 7 items: Ways = 7! / (2! × 2!) = 5040 / 4 = 1260. Step 2: Arrange 4 vowels within [V]: A, A, E, E. Ways = 4! / (2! × 2!) = 24 / 4 = 6. Total arrangements = 1260 × 6 = 7560.
Which of the following symbols should replace the sign (@) and (%) respectively in the given expression in order to make the expression C ≥ G and A >...
Statements: G > P > Y ≥ E = N ≥ Q ≥ Z
Conclusions:
I. P > Z
II. Q ≤ YStatements: M > L = K ≥ H, V > G > M, U < N = H
Conclusions:
I. V > U
II. H < G
III. L ≥ V
In the following question the relationship between different elements is given in the statements followed by three conclusions I, II and III. Read the...
Statements: Z ≤ O = Q < P; A = X > M = Y ≥ P
Conclusions:
I. A > O
II. Z < X
III. Q ≤ M
In the question, assuming the given statements to be true, find which of the conclusion (s) among given three conclusions is/are definitely true and th...
Statements: N $ Q, Q @ M, M % S, S % T
Conclusions : I. S # Q II. S & Q III. M & T
...Statements: Z % Y; X # W; U % V; W & V; Y @ X
Conclusions:Â Â Â Â Â
I. U @ X 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:
P > O ≥ D > M ≤ Y < L; M > G > Q
Conclusions:
I)Â O > Q
II) L < G
...Statements: R ≥ S > T; U < V ≤ T; V > W
Conclusions:
I. R > V
II. W < S
 III. T > W
