The answer is 10 over 3 (you write 10 over 3, without a fraction line in between, and with parentheses around the entire expression). This is calculated as (10 x 9 x 8) / (1 x 2 x 3).
There are 5040 ways.
Well, honey, there are 30 students in the class, and you want to choose a group of 3. So, you're looking at a classic combination situation. The formula for combinations is nCr = n! / r!(n-r)!, so in this case, it's 30C3 = 30! / 3!(30-3)! = 4060 ways to choose those 3 lucky students. It's like picking the winning lottery numbers, but with fewer tears and more math.
7
20*19*18*17*16 = 1860480 ways.
This number is 19(52)(52-1)(52-2)(52-3)(52-4)(52-5)(52-6)(52-7), or approximately 5.89 X 1014. The reasoning is as follows: Any one of the 19 freshman can be selected first. After this choice is made, there are 52 remaining persons (34 + 19 -1) from among whom the second position on the committee can be chosen, 52 -2 remaining persons for the third position, etc.)
6,375,600
125
53,130 ways.
There are 10 different sets of teachers which can be combined with 4 different sets of students, so 40 possible committees.
There are 9*8*7 = 504 ways.
There are 11880 ways.
309*308/2 = 47586
The first member chosen can be any one of 1,514 students.The second member chosen can be any one of the remaining 1,513 students.The third member chosen can be any one of the remaining 1,512 students.So there are (1,514 x 1,513 x 1,512) ways to choose three students.But for every group of three, there are (3 x 2 x 1) = 6 different orders in which the same 3 can be chosen.So the number of `distinct, unique committees of 3 students is(1514 x 1513 x 1512) / 6 = 577,251,864
36 x 35/2 ie 630
20 * 19 * 18 * 17 = 116,280 ways This is Permutation: nPr = n! / (n-r)!
I'm going with 25,200 3 men out of 10 may be chosen in 10C3 ways = 10 ! / 3! 7 ! = 120 ways. 4 women may be chosen out of 10 in 10C4 = 10 ! / 4! 6! ways = 210 ways. Therefore, a committee with 3 men and 4 women can be formed in 120 x 210 = 25,200 ways.
40 x 39 x 38 x 37 = 2193360