...Find the number of combinations of (n) things taken 3 together, and write down the expression for the number of combinations of (n) things taken (r) together. The number of combinations of (n) things taken (4) at a time is to the number taken (2) at a time as 15 : 2, find n. MATHEMATICS. Voluntary...

...with Art. 405, any combination of n things may be made into 1 . 2 . 3 ... n permutations. 408. To find the number of combinations of n different things taken r at a time. Let Cr denote the number of combinations required. Since each combination contains r things it can...

...kind), q all alike (of another kind), r all alike (of another kind), and the rest all different, VI. The number of combinations of n different things, taken r at a time, _n(nl) (n-2}...(n- r+l) \rfn - r ' VII. The total number of combinations of n different things = 2"-l....

...together when / of them are of one kind, q of another, r of another, and the rest all different \n 80. The number of combinations of n different things, taken r at a time . . _ n(n—i)(n — 2) .... (n — r+i) ' ----- ' 17 | r | n— r 81. The total number of combinations...

...number of combinations of n different things r at a time is denoted by the symbol KGr. 240. To find the number of combinations of n different things taken r at a time. Let the different things be represented by the letters a, b, c... Now in the combinations of the n...

...which 6 persons can be seated at a dinner table. Ans. 720. 181. The Number of Combinations. — To find the number of combinations of n different things taken r at a time. The number of permutations of n things taken r at a time is n(n - l)(n - 2) ....... (n - r + 1). (Art....

...n — r at a time, is |n In r. or |n — r\n — (n — r)' |w — r\r 2 ' But this is the same as the number of combinations of n different things taken r at a time. Q Hence, the number of combinations of n different things takeni r at a time is equal to the number...

...which are only four in number. The number of their permutations is 24 ; and so on. Hence, in general, The number of combinations of n different things taken r at a time, multiplied by |_r, is equal to the number of permutations. Notes: 1. Combinations differ from permutations...

...term of an AP is — 2, and the sum of the first 8 terms is — 10, find the nth term. 9. Show that the number of combinations of n different things taken r at a time can be found independently of the number of permutations. 10. (a) Deduce the formula called the Binomial...

...rationalize the following expressions : — (a.) a + b*. *T\ "AI 7i2.l 5 (c.) a* + 6* + c*. (40.) 50. Find the number of combinations of n different things, taken r at a time, without assuming the formula for the number of permutations. Out of 40 consecutive integers in how...