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 a student select the questions?

Asked by Abhisek | 1 year ago |  126

##### Solution :-

Given: 12 Qs are divided into 2 parts – Part I and Part II consisting of 5 and 7 Qs respectively. A student must attempt 8 Qs with atleast 3 from each part. This can be done as:

(a) 3 Qs from part I and 5 Qs from part II.

(b) 4 Qs from part I and 4 Qs from part II.

(c) 5 Qs from part I and 3 Qs from part II.

The first case can be selected in $$^5C_3\times ^7C_5$$ ways.

The second case can be selected in $$^5C_4\times ^7C_4$$ ways.

The third case can be selected in $$^5C_5\times ^7C_3$$ ways.

Thus, number of ways of selecting Qs

$$^5C_3\times ^7C_5+ ^5C_4\times ^7C_4+ ^5C_5\times ^7C_3$$

$$\dfrac{5!}{3!2!}\times \dfrac{7!}{2!5!}+\dfrac{5!}{1!4!}\times \dfrac{7!}{4!3!}+\dfrac{5!}{5!0!}\times \dfrac{7!}{3!4!}$$

= 210 +175 + 35 = 420

Answered by Pragya Singh | 1 year ago

### Related Questions

#### How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?

How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?

#### Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.

Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.

#### How many words, with or without meaning can be formed from the letters of the word ‘MONDAY’,

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

(i) 4 letters are used at a time

(ii) all letters are used at a time

(iii) all letters are used but first letter is a vowel ?