4 boys and 2 girls are to be seated in a row in such a way that the two girls are always together. In how many different ways can they be seated?

Let the no. of girls be 5x No. of boys=7x According to the question 5x+8=7x 7x-5x=8 2x=8 x=8/2 x=4 No. of girls=5*4=20 no. of boys=7*4 or 5*4+8=28 Hence the total strength of the class is 20+28=48

Let us denote 2 boys and 2 girls in room X as B1, B2 and G1, G2 respectively. Let us denote 1 boy and 3 girls in room Y as...

Leaving one seat vacant between two boys may be seated in 4! ways. Then at remaining 5 seats, 5 girls any sit in 5! ways. Hence the required number =...

(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...

(a) Reqd. number = 4! × 2! = 24× 2 = 48

(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...

(a) Total number of students = 1224 Total number of girls = 600 Total number of boys = 1224 - 600 = 624 Required ratio = 624 :600 = 26 : 25

(b) First letter can be dropped into any of the 3 boxes. It can be done in 3 ways. Similarly second letter can also be dropped into any of the...

(d) Total no of ways of arrangement for six players = 6! Let us take Ajit and Mukerjee as one entity. So now there are (6 – 2 + 1)...

(b) Take, A and B to be always together as a single entity. Now, total no. of children = 4 – 2 + 1 = 3 These can be arranged...