Mark the correct alternative in the following:

The number of ways in which a host lady can invite for a party of 8 out of 12 people of whom two do not want to attend the party together is

A.

B.

C.

D. none of these

There are 10 persons named P₁, P₂, P₃,……P₁₀. Out of 10 persons, 5 persons are to be arranged in a line such that is each arrangement P₁ must occur whereas P₄ and P₅ do not occur. Find the number of such possible arrangements.

How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?

A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of :

at least 3 girls?

How many words, with or without meaning can be formed from the letters of the word ‘MONDAY’, assuming that no letter is repeated, if

4 letters are used at a time

A parallelogram is cut by two sets of m lines parallel to its sides. Find the number of parallelograms thus formed.

How many words, with or without meaning can be formed from the letters of the word ‘MONDAY’, assuming that no letter is repeated, if

all letters are used at a time

In an examination, a question paper consists of 12 questions divided into two parts, i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can help a student select the questions?

Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (i) straight lines (ii) triangles can be formed by joining them?

A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of :

at most 3 girls?

How many words, with or without meaning can be formed from the letters of the word ‘MONDAY’, assuming that no letter is repeated, if

all letters are used but the first letter is a vowel?