1.

(i) Prove that: ""^(n)P_(r) = ""^(n-1)P_(r) + r. ""^(n-1)P_(r–1) (ii) If ""^(20)C_(r+2) = ""^(20)C_(2r–3) find ""^(12)C_(r) (iii) Find the ratio ""^(20)C_(p) "to"""^(25)C_(r) when each of them has the greatest value possible. (iv) Prove that ""(n-1)C_(3) + ""^(n-1)C_(4) gt""^(n)C_(3) if n> 7 (v) Find r if ""^(15)C_(3r) = ""^(15)C_(r+3 )

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ANSWER :ii. 792. (III) `(143)/(4025)`; (v) r = 3


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