Tamil Nadu Board of Secondary EducationHSC Science Class 11

Find the total number of subsets of a set with[Hint: nC0 + nC1 + nC2 + ... + nCn = 2n] 5 elements - Mathematics

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Sum

Find the total number of subsets of a set with
[Hint: nC0 + nC1 + nC2 + ... + nCn = 2n] 5 elements

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Solution

Subsets with 5 elements:

Number of subsets with no element = 5C0

Number of subsets with one element = 5C1

Number of subsets with 2 elements = 5 C2

Number of subsets with 3 elements = 5C3

Number of subjects with 4 elements = 5C4

Number of subsets with 5 elements = 5C5

Total number of subjects

= 5C0 + 5C1 + 5C2 + 5C3 + 5C4 + 5C5

= `1 + (5!)/(1!(5 - 1)!) + (5!)/(2!(5 - 2)!) + (5!)/(3!(5 - 3)!) + (5!)/(4!(5 - 4)!) + 1`

= `1 + (5!)/(4!) + (5!)/(2!  3!) + (5!)/(3!  2!) + (5!)/(4!) + 1`

= `1 + (5 xx 4!)/(4!) + (5 xx 4 xx 3!)/(2! xx 3!) + (5 xx 4 xx 3!)/(3! xx 2!) + (5 xx 4!)/(4!) + 1`

= `1 + 5 + (5 xx 4)/(2 xx 1) + (5 xx 4)/(2 xx 1) + 5 + 1`

= 6 + 10 + 10 + 6

= 32 

Concept: Combinations
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Chapter 4: Combinatorics and Mathematical Induction - Exercise 4.3 [Page 186]

APPEARS IN

Tamil Nadu Board Samacheer Kalvi Class 11th Mathematics Volume 1 and 2 Answers Guide
Chapter 4 Combinatorics and Mathematical Induction
Exercise 4.3 | Q 10. (ii) | Page 186

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