...pression by I n — r it becomes . — : - . 1 * L - rn — r 495. The number of combinations of n things taken r at a time is the same as the number of them taken n — r at a time. The number of combinations of n things taken nr at a time is w(n _!)(«-...

...denominator of this expression by ! n — r it becomes - — *= . 495. The number of combinations of n things taken r at a time is the same as the number of them taken n — r at a time. The number of combinations of n things taken n — r at a, time is...

...\r.Cr---n(nl) (n-r+1); „ _ n(nl) (n-r+I) .. .,- - • ^ 409. To shew that the number of combinations of n things taken r at a time is the same as the number taken n- r ni u time. r =n.(»-I) (nr + 1). "~ 1.2.3 r ' „ n.(nl) {n-(nr) + l} **-*- 1.2.3 (nr) _n.(nl) (r +...

...[r.Cr—-n(n — 1) (n— r+l); „ _и(п-1) (n-r+1) 409. To shew that the number of combinations of n things taken r at a time is the same as the number taken n — r at a time. „ _n.(n— 1) (и -r + l) and CL -= 410. Making r=l, 2, 3 i — 1, r, r+1 in order, rr - nn w-1 /yn...

......... (n-r+l); n(nl) ...... (n. c= \r 409. To show that the number of combinations of n things taken i at a time is the same as the number taken n — r at a time. _n.(nl) (ro-'r+1) . 1.2.3 ...... (nr) _n.(nl) ...... (r + 1) 1.2.3 ...... (nr) ' Hence 0, __ n.(nl)...

...and c, d, e in н. р., prove that a, c, e are in Q. p. 10. Shew that the number of combinations of n things taken r at a time is the same as the number taken n—r at a time. EXEEOISE— XCII. 1. Divide ¿r4-a4+2a¿r3+2wa3¿r-(w2-1)aV by x2+а?-(п-1)аx. 2....

...(n-r+1); . - n(nl) ...... (n-r+1) ' -------- ------ 409. To show that the number of combinations of n things taken r at a time is the same as the number taken nr at a time. n.(nl) ...... (n-r+l). °'~ 1.2.3 ...... r r O'~ 1.2.3 ...... (nr) = 1.2.3 ...... (nr)...

....-. lr.Cr=»(nl) (n-r+l); . n(n-1) (n-r+1) 409. To show that the numbcr of combinations of n thingt taken r at a time is the same as the number taken n — r at a time. n.(nl) (n-r+1) C' = 1.2.3 r ' . „ n.(nl) )n-(nr) + l| and C"-= — 1-2.3 (nr) —n.(nl) (r + 1) =...

...(n-r+l); . „ n(nl) _ (n .• " 409. To show that the number of combinations of n things taken r ai a time is the same as the number taken n - r at a time. n.(и-1) _ (n-r+l). v'~ 1.2.3 _ r ' ' _n.(nl) _ {n-(п and .V,_ 1.2.3 _ (nr) ' Hence Jjl_ _ п.(n-1)...

...true for r = n, the symbol |^0 must be considered as equivalent to 1. The number of combinations of n things taken r at a time is the same as the number of them taken n — r at a time. For the number taken n — r at a time is, from (2), n — rn —...