Permutations and Combinations

The number of words that can be formed by using the letters of the word CALCULATE such that each word starts and ends with a consonant, are

Five students are to be arranged on a platform such that the boy \(B_1\) occupies the second position and such that the girl \(G_1\) is always adjacent to the girl \(G_2\). Then, the number of such possible arrangements is

The teacher wants to arrange 5 students on the platform such that the boy \(B_1\) occupies second position and the girls \(G_1\) and \(G_2\) are always adjacent to each other, then the number of such arrangements is

A group consists of 8 boys and 5 girls, then the number of committees of 5 persons that can be formed, if committee consists of at least 2 girls and at most 2 boys, are

If a question paper consists of 11 questions divided into two sections I and II. Section I consists of 6 questions and section II consists of 5 questions, then the number of different ways can student select 6 questions, taking at least 2 q...

A committee of 5 is to be formed out of 6 men and 4 ladies. The number of ways this can be done, when at most 2 ladies are included, is

Out of 7 consonants and 4 vowels, the number of words consisting of 3 consonants and 2 vowels are

A polygon has 44 diagonals. Then the number of sides of the polygon are

The numbers can be formed using the digits \(1,2,3,4,3,2,1\) so that odd digits always occupy odd places in __________ ways.

The number of ways in which 8 different pearls can be arranged to form a necklace is

For a set of five true or false questions, no student has written the all correct answers and no two students have given the same sequence of answers. The maximum number of students in the class for this to be possible is

All the letters of the word 'ABRACADABRA' are arranged in different possible ways. Then the number of such arrangements in which the vowels are together is

If \(\frac{n !}{2 !(n-2) !}\) and \(\frac{n !}{4 !(n-4) !}\) are in the ratio \(2: 1\), then \(n=\)