Permutations and Combinations

The number of natural numbers, between 212 and 999, such that the sum of their digits is 15, is .

Let S=\p1,p2 ,p10\ be the set of first ten prime numbers. Let A=S P, where P is the set of all possible products of distinct elements of S. Then the number of all ordered pairs (x,y), x S, y A, such that x divides y, is .

The number of 3-digit numbers, that are divisible by 2 and 3, but not divisible by 4 and 9, is .

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

The number of integers, between 100 and 1000 having the sum of their digits equal to 14, is .

The number of 3-digit numbers, formed using the digits 2, 3, 4, 5 and 7, when the repetition of digits is not allowed, and which are not divisible by 3 , is equal to .