How many ways are there to select 12 countries in the United Nations to serve on a council if 3 is selected from a block of 54, 1 are selected from a block of 62 and 8 are selected from the remaining 73 countries?
2007-04-30 20:22:08 · 4 answers · asked by Cloud Nine 1 in Science & Mathematics ➔ Mathematics
C(54, 3) * C(62, 1) * C(73, 8)
= 24804 * 62 * 13442126049
= 2070194948554392.
Fernando A has made an error calculating C(73, 8). The 65 in the numerator should not be there, so his answer is a factor of 65 too high.
2007-04-30 20:38:30 · answer #1 · answered by Scarlet Manuka 7 · 2⤊ 0⤋
simple take C as combination, then
xCy = x!/(y!*(x-y)!)
the number of ways = 54C3 * 62C1 * 73C8
solve the combinations one by one
54C3 = 54!/(3!*51!) = 54*53*52/6 = 24804
62C1 = 62!/(1!*61!) = 62
73C8 = 73!/(8!*65!) = 73*72*71*70*69*68*67*66/(8*7*6*5*4*3*2*1)
= 13442126049
the number of ways :
= 24804 * 62 * 13442126049
= 2.07E+016
so many ways, isn't it?
PS if you find it helpful, a best answer badly needed
2007-04-30 20:37:09 · answer #2 · answered by Anonymous · 1⤊ 1⤋
13442150915
2007-04-30 20:35:05 · answer #3 · answered by Manik 7 · 0⤊ 1⤋
(12)/((3C54)(1C62)(8C73))
2007-04-30 20:30:13 · answer #4 · answered by joseph 2 · 0⤊ 2⤋