Q. 254.2( 5 Votes )

# 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?

Answer :

A student has to attempt 8 questions in total and at least 3 from each part.

There can be three cases:

**Case 1:** 3 from part 1 and 5 from part 2

^{5}C_{3} × ^{7}C_{5}

= 10× 21

= 210 ways

**Case 2:** 4 from part 1 and 4 from part 2

^{5}C_{4} × ^{7}C_{4}

= 5× 35

= 175 ways

**Case 3:** 5 from part 1 and 3 from part 2.

^{5}C_{5} × ^{7}C_{3}

= 35 ways

So total ways = 210 + 175 + 35

= 420 ways

Rate this question :

Prove that the product of 2n consecutive negative integers is divisible by (2n)!

RD Sharma - MathematicsThere are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated.[Hint: Required number = 210 – 1].

Mathematics - ExemplarIf ^{n+1}C_{r+1} : ^{n}C_{r} = 11 : 6 and ^{n}C_{r} : ^{n–1}C_{r–1} = 6 : 3, find n and r.

If ^{n}C_{r–1} = 36, ^{n}C_{r} = 84 and ^{n}C_{r+1} = 126, find r.

Fill in the Blanks

If ^{n}P_{r} = 840, ^{n}C_{r} = 35, then r = ______.

The number of ways in which a team of eleven players can be selected from 22 players always including 2 of them and excluding 4 of them is

Mathematics - Exemplar