(b) Treat B and T as a single letter. Then the remaining letters (5 + 1 = 6) can be arranged in 6! ways. Since, O is repeated twice, we have to divide by 2 and the B and T letters can be arranged in 2! ways.
(e) The word SIGNATURE consists of nine letters comprising four vowels (A, E, I and U) and five consonants (G, N, R, T and S). When the four vowels are...
(d) Assume the 2 given students to be together (i.e one].
Now there are five students.
Possible ways of arranging them are = 5! = 120
Now, they (two girls) can arrange themselves...
(e) 3 vowels can be arranged in three odd places in 3!ways. Similarly, 3 consonants can be arranged in three even places in 3! ways. Hence, the total number of...
(c) Taking all vowels (IEO) as a single letter (since they come together) there are six letters
Hence no. of arrangements = 6!/2!x3!=2160
[Three vowels can be arranged 3! ways among
themselves, hence...
(b) Required number of possible outcomes
= Total number of possible outcomes –
Number of possible outcomes in which all vowels are together
= 6 ! – 4 ! × 3 != 576
