...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....

....... (n-r+1) (464); _я(я-1)(я-й)(п-3) ---- (nr .. Or_ r; 469. The number of combinations of n things, taken r at a time, is equal to the number of combinations of n things, taken n — r at a time. Denote the number of combinations of n things, taken n — r at a...

...5 is to 18. Find the value of n. Ans. n = 12. 3. If the number of permutations of n things, taken 3 at a time, is equal to the number of combinations of n things, taken 4 at a time, what is the value of n ? Ans. n — 7. 4. Of 9 things, how many must be...

...the number of n things taken r at a time.* r+l 5. The number of the combination» of n things when taken r at a time is equal to the number of combinations of the same n thing» when they are taketi •}i—r at a time.\ * To find the number of combinations...

...the number of n things taken r at a time.* r-\-\ 5. The number of the combination* of n things when taken r at a time is equal to the number of combinations of the same n things when they are taken M—r at a time.\ * To ßnd tfic number of combinations thai...

...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...

...a? — 3* + 9 = 0. (35.) 44. Show from first principles that the number of combinations of n things r at a time is equal to the number of combinations of (n — 1) things r at a time, together with the number of combinations of ('» — 1) things (r — 1)...

...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....

...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...