Permutations and Combinations

The number of ways, 5 boys and 4 girls can sit in a row so that either all the boys sit together or no two boys sit together, is .

From all the English alphabets, five letters are chosen and are arranged in alphabetical order. The total number of ways, in which the middle letter is ' M ', is :

1. 6084
2. 5148
3. 14950
4. 4356

In a group of 3 girls and 4 boys, there are two boys B1 and B2. The number of ways, in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but B1 and B2 are not adjacent to each other, is :

1. 120
2. 96
3. 72
4. 144