No. of elements

BITSAT 2015 Guidance › Algebra questions › No. of elements

If x = {1,2,3,..............., 100} and let S = {(a,b,c) | a,b,c belongs to a < b and a <c }, then the number of elements in S are :
(a) 328250 (b) 328450 (c)328350 (d) none

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5 Answers

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Hari Shankar ·2009-11-14 01:36:15

Consider the subsets of X with three elements.

Of these 1/3 rd have this property

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iitimcomin ·2009-11-14 06:20:36

is it c???

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Tush Watts ·2009-11-14 06:22:44

yeah it's (c)

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iitimcomin ·2009-11-14 06:28:00

EXP. GOES LIKE THIS .......

i can select 3 elements ...

case 1 ..

3 distinct elements ...

total no. of ways ..

100C3 ...

now these three elements i can arrange in such a way that a<b<c

or a<c<b

hence total ways .... 2(100C3) ..

case 2 ..

2 elements same ...

total ways ..

100C2 ...

i can arrange each set picked only in 1 way

case1+case2 = 100C2 + 2(100C3) ....

[1]

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Tush Watts ·2009-11-14 06:32:20

Thanx a lot [1]

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Basic Integral Calculus Operators Symbols Matrix Cases

√ √ || {} [] () → ~ ^ x x x → → ln log lg lim lim cos sin tan cot arcsin arccos arctan

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∑ ∑ ∑ ∑ ∑ ∮ ∮ ∮ ∮ ∮ ∏ ∏ ∏ ∏ ∏ ∐ ∐ ∐ ∐ ∐

+ - × ÷ ± ∓ = ∪ ∩ ≠ ∼ ≈ ∅ ∀ ∃ ∈ ∋ ∝ ≤ ≥ ≃ ≅ ≡ < > ≪ ≫ ⊂ ∉ ⊃ ⊆ ⊇ ⇒ ⇐ ⇔ ⇒ ⇐ ⇔ ⇑ ⇓ ⇕ → ← ↔ → ← ↔ ↑ ↓ ↕ ↖ ↗ ↘ ↙ ↪ ↩ ⇀ ↼ ⇁ ↽

° ∂ ∞ α β γ δ θ λ μ ν ξ π ρ σ φ ω ε ƒ κ τ υ Γ Δ Λ Σ Π Ω

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No. of elements

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