n </span>'/\html'<span class="right_angle">n-r</span>'=2520...(i) and C(n, r) = 21 \Rightarrow\html'<span class="right_angle">n </span>'/{\html'<span class="right_angle">r</span>'\html '<span class="right_angle">n-r</span>'}=21.....(ii) From dividing (i) by (ii) we get \html '<span class="right_angle">n </span>'/\html '<span class="right_angle">n-r</span>'\times{\html '<span class="right_angle">r </span>'\html '<span class="right_angle">n-r</span>'}/\html '<span class="right_angle">n</span>'=2520/21 \html '<span class="right_angle">r </span>'=360/3=120 \html '<span class="right_angle">5</span>'=5\cdot4\cdot3\cdot2\cdot1=120 \Rightarrowr=5 From (i)\html '<span class="right_angle">n </span>'/\html '<span class="right_angle">n-5</span>'=2520 \Rightarrow{n(n-1)(n-2)(n-3)(n-4)\html '<span class="right_angle">n-5</span>'}/\html '<span class="right_angle">n-5</span>'=2520\Rightarrown(n–1)(n–2)(n–3)(n–4)=2520 \Rightarrow7\times6\times5\times4\times3\times2=2520 ∴n=7 Now, C(n+1,r+1)=C(7+1,5+1) =C(8-6)=\html '<span class="right_angle">8</span>'/{\html '<span class="right_angle">6</span>'\html '<span class="right_angle">8-6</span>'} =\html '<span class="right_angle">8</span>'/{\html '<span class="right_angle">6</span>'\html '<span class="right_angle">2</span>'}={8\times7}/2=4\times7=28" >
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NDA Math Permutations and Combinations

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