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Message: <blockquote data-quote="djHiran" data-source="post: 10282413" data-attributes="member: 6429"><p><span style="color: Sienna"><span style="font-size: 15px">Well... this is going to need a lengthy answer for sure.</span></span></p><p><span style="color: Sienna"><span style="font-size: 15px"></span></span></p><p><span style="color: Sienna"><span style="font-size: 15px">There are 3 broad ways to select 4 numbers out of {1,2,3,4,5,6,7,8,9} so that their sum is even...</span></span></p><p><span style="color: Sienna"><span style="font-size: 15px"></span></span></p><p><span style="color: Sienna"><span style="font-size: 15px">1. Four even numbers</span></span></p><p><span style="color: Sienna"><span style="font-size: 15px">2. Two even and two odd</span></span></p><p><span style="color: Sienna"><span style="font-size: 15px">3. Four odd numbers</span></span></p><p><span style="color: Sienna"><span style="font-size: 15px"></span></span></p><p><span style="color: Sienna"><span style="font-size: 15px">For the first category, we accomplish the result by further subdividing the ways as...</span></span></p><p><span style="color: Sienna"><span style="font-size: 15px"></span></span></p><p><span style="color: Sienna"><span style="font-size: 15px">1.1  Four distinct numbers from {2,4,6,8} : Ways:= ⁴C₄ = 1</span></span></p><p><span style="color: Sienna"><span style="font-size: 15px">1.2  Two same, two distinct : Ways := ⁴C₁ x ³C₂ = 12</span></span></p><p><span style="color: Sienna"><span style="font-size: 15px">1.3  Two same, another two same : Ways := ⁴C₁ x ³C₁ = 12</span></span></p><p><span style="color: Sienna"><span style="font-size: 15px">1.4  Three same, one different := ⁴C₁ x ³C₁ = 12</span></span></p><p><span style="color: Sienna"><span style="font-size: 15px">1.5  All same : Ways := ⁴C₁ = 1</span></span></p><p><span style="color: Sienna"><span style="font-size: 15px"></span></span></p><p><span style="color: Sienna"><span style="font-size: 15px">For the second category,....</span></span></p><p><span style="color: Sienna"><span style="font-size: 15px"></span></span></p><p><span style="color: Sienna"><span style="font-size: 15px">2.1  Distinct even, distinct odd from {1,3,5,7,9} : Ways = ⁴C₂ x ⁵C₂ = 60</span></span></p><p><span style="color: Sienna"><span style="font-size: 15px">2.2  Distinct even, same odd : Ways := ⁴C₂ x ⁵C₁ = 30</span></span></p><p><span style="color: Sienna"><span style="font-size: 15px">2.3  Same even, distinct odd : Ways := ⁴C₁ x ⁵C₂ = 40</span></span></p><p><span style="color: Sienna"><span style="font-size: 15px">2.4  Same even, same odd : Ways := ⁴C₁ x ⁵C₁ = 20</span></span></p><p><span style="color: Sienna"><span style="font-size: 15px"></span></span></p><p><span style="color: Sienna"><span style="font-size: 15px">For the third...</span></span></p><p><span style="color: Sienna"><span style="font-size: 15px"></span></span></p><p><span style="color: Sienna"><span style="font-size: 15px">3.1  Four distinct numbers from {1,3,5,7,9} : Ways:= ⁵C₄ = 5</span></span></p><p><span style="color: Sienna"><span style="font-size: 15px">3.2  Two same, two distinct : Ways := ⁵C₁ x ⁴C₂ = 30</span></span></p><p><span style="color: Sienna"><span style="font-size: 15px">3.3  Two same, another two same : Ways := ⁵C₁ x ⁴C₁ = 20</span></span></p><p><span style="color: Sienna"><span style="font-size: 15px">3.4  Three same, one different := ⁵C₁ x ⁴C₁ = 20</span></span></p><p><span style="color: Sienna"><span style="font-size: 15px">3.5  All same : Ways := ⁵C₁ = 5</span></span></p><p><span style="color: Sienna"><span style="font-size: 15px"></span></span></p><p><span style="color: Sienna"><span style="font-size: 15px">Therefore the total successful ways to obtain an even sum is, q = 268</span></span></p><p><span style="color: Sienna"><span style="font-size: 15px"></span></span></p><p><span style="color: Sienna"><span style="font-size: 15px">But the total ways to select a random sample of size 4 from the set {1,2,3,4,5,6,7,8,9} is, Q = 9⁴ = 6561</span></span></p><p><span style="color: Sienna"><span style="font-size: 15px"></span></span></p><p><span style="color: Sienna"><span style="font-size: 15px">Therefore the probability one gets an even sum is, </span></span></p><p><span style="color: Sienna"><span style="font-size: 15px"></span></span></p><p><span style="color: Sienna"><span style="font-size: 15px">P = q / Q </span></span></p><p><span style="color: Sienna"><span style="font-size: 15px">= 268 / 6561 </span></span></p><p><span style="color: Sienna"><span style="font-size: 15px">= 0.04085</span></span></p></blockquote><p></p>

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