# C(n,r)=C(r,r)⋅C(n−r,0)+C(r,r−1)⋅C(n−r,1)+C(r,r−2)⋅C(n÷r,2)+C(r,r−3):C(n−r,3)++C(r,1)⋅C(a−r,r−1)+C(r,0)⋅C(n−r,r)

Question
Probability
C(n,r)=C(r,r)⋅C(n−r,0)+C(r,r−1)⋅C(n−r,1)+C(r,r−2)⋅C(n÷r,2)+C(r,r−3):C(n−r,3)++C(r,1)⋅C(a−r,r−1)+C(r,0)⋅C(n−r,r)

2020-12-26
Suppose that you have n objects, and you line them up. You need to pick r objects. If you take r objects from the first r objects, then you need to take 0 objects from the rest of the objects, which you have n—r. Thus, you have O(r,r)- C(n—r,0) ways of doing this.
Similarly, if you pick k objects from the first r objects, you need to take r —k objects from the rest of the objects. You have O(r, k)-C(n—r,r—k) ways of doing this.
Since you can take Q, 1, ..., r objects from the first r objects, we have that 0
ways. Thus we have proven that PSKr C(n,r)=∑ C(r,k)*C(n-r,r-k) k=0ZSK
which we needed to prove.

### Relevant Questions

The unstable nucleus uranium-236 can be regarded as auniformly charged sphere of charge Q=+92e and radius $$\displaystyle{R}={7.4}\times{10}^{{-{15}}}$$ m. In nuclear fission, this can divide into twosmaller nuclei, each of 1/2 the charge and 1/2 the voume of theoriginal uranium-236 nucleus. This is one of the reactionsthat occurred n the nuclear weapon that exploded over Hiroshima, Japan in August 1945.
A. Find the radii of the two "daughter" nuclei of charge+46e.
B. In a simple model for the fission process, immediatelyafter the uranium-236 nucleus has undergone fission the "daughter"nuclei are at rest and just touching. Calculate the kineticenergy that each of the "daughter" nuclei will have when they arevery far apart.
C. In this model the sum of the kinetic energies of the two"daughter" nuclei is the energy released by the fission of oneuranium-236 nucleus. Calculate the energy released by thefission of 10.0 kg of uranium-236. The atomic mass ofuranium-236 is 236 u, where 1 u = 1 atomic mass unit $$\displaystyle={1.66}\times{10}^{{-{27}}}$$ kg. Express your answer both in joules and in kilotonsof TNT (1 kiloton of TNT releases 4.18 x 10^12 J when itexplodes).
A manufacturer of digital phones has the following probability distribution for the number of defects per phone: xf(x) .89 1.07 2.03 3.01
(a) Determine the probability of 2 or more defects. (b) Is a randomly selected phone more likely to have 0 defects or 1 or more defects?
If you used a random number generator for the numbers from 1 through 20 to play a game, what is the theoretical probability of getting each of these outcomes? a. A multiple of 3 or a multiple of 7, P(multiple of 3 or multiple of 7) b. P( even or odd) c. P(prime or 1) d. How did you find the probabilities of these events?
The diagram shows a spinner. When the arrow is spun the probability of scoring a 2 is 0.3 . The arrow is spun twice and the scores are added. What is the probability that the total score is 6?6? Express the answer as a decimal. [ \sqrt { 2 } \text { . } ]