Permutations and Combinations

Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited for a picnic if 5 of them must be from group A and the remaining 3 from group B, is equal to :

1. 8925
2. 9100
3. 8575
4. 8750

The number of words, which can be formed using all the letters of the word "DAUGHTER", so that all the vowels never come together, is :

1. 34000
2. 37000
3. 35000
4. 36000

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