7c6
-3c2
Six 3x2=6 atoms, in 3 molecules of H2
It represents number of moles of an element.
3c2+2c2+3c1 2c1 --------------- 7c2. I have done it this way. 3C2 means that the both balls would be green 2C2 both would be red and 3C1 and 2C1 because both the balls can be red and green.
You can find them at http://www.hystar.com.tw/hydraulic/hydraulic_2.htm there is an option to buy online even for that
The answer is 3C2*4C4*5C2 = [3 * 1 * (5*4)/(2*1)] = 3*1*10 = 30 ways.
By using the 3 digits of a number we can form 3 different two digit numbers. 3C2 = 3!/[(3 - 2)!2!] = 3!/(1!2!) = (3 x 2!)/2! = 3
it means combinatorial or combination, you use the formula nCr = n!/((n-r)! x r!). example 5c3 = 5! / ((5-3)! x 3!) = 5! / (2! x 3!) = (5x4x3x2x1) / ((2x1) x (3x2x1)) = 10
If the probability of winning with one lottery ticket is P(W) = 1/(179 x 106) and is independent of the number of tickets sold, and you buy 3 tickets, then you have:The probability of not winning (loosing) of one ticket is P(L) = 1 - 1/(179 x 106).The probability of all 3 tickets loosing is P(3L) = [P(L)]3 = [1 - 1/(179 x 106)]3 =0.999999983...The probability of two loose one win is P(2L1W) = 3C2 [P(L)]2 P(W)P(2L1W) = 3[1 - 1/(179 x 106)]2∙[1/(179 x 106)] = 1.675977635... x 10-8 == 1/(5.966666733... x 107), which is about 1 in 59.7 million.The probability of one loose two win is P(1L2W) = 3C2 P(L) [P(W)]2P(1L2W) = 3[1 - 1/(179 x 106)][1/(179 x 106)]2 = 9.363003599... x 10-17 == 1/(1.068033339... x 1016), which is about 1 in 10 680 333 billion, (≈ 1 in 10.7quadrillion).The probability of three win is P(3W) = [P(W)]3 = [1/(179 x 106)]3 == 1.743576099... x 10-25 = 1/(5.735339... x 1024), which is about 1 in 5.7 septillion.
1 x 231, 3 x 77, 21 x 11, 33 x 7. Add the digits and you get 6, which means it is divisible by 3. (3 x 77) 77 has two prime factors, 7 and 11. So you can multiply any combination of the factors to get 231. 3C2 (3 choose 2) in Pascal's triangle is 3, which means there are three possible combinations. Oh, yeah, and you can always just do 1 x 231.
The apothem is the radial distance from the middle of the side to the centre of the hexagon. A hexagon is six congruent equilateral triangles joined by adjacent sides. Equilateral triangles can be divided into two equal right angled triangles. The upright of the right angled triangle is effectively the apothem of the original hexagon. Pythagoras now kicks in. The apothem (vertical) is A and half the side length (base) is B, the third (longest) side is C and is the same as the original side length. Pythagoras states A2 + B2 = C2. So by transposition, A = root (C2 - B2). As B = 1/2 C, the apothem A is given by: A = root(C2 - (C/2)2) = root(C2 - C2/4) = root(3C2/4) = C x root(3) / 2 So the apothem of a hexagon is 1/2 x root(3) x the side length.