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Prove that nCr plus nCr minus 1 equals n plus 1Cr?
nCr + nCr-1 = n!/[r!(n-r)!] + n!/[(r-1)!(n-r+1)!] = n!/[(r-1)!(n-r)!]*{1/r + 1/n-r+1} = n!/[(r-1)!(n-r)!]*{[(n-r+1) + r]/[r*(n-r+1)]} = n!/[(r-1)!(n-r)!]*{(n+1)/r*(n-r+1)]} = (n+1)!/[r!(n+1-r)!] = n+1Cr
General formulae for the combination nCr in terms of n and r?
nCr=n!/(r!(n-r)!)
How do you find the coefficients of the terms in the binomial expansion?
The coefficient of x^r in the binomial expansion of (ax + b)^n isnCr * a^r * b^(n-r)where nCr = n!/[r!*(n-r)!]
How many combinations of 5 numbers are there for 1-30?
To calculate the number of combinations of 5 numbers chosen from 1 to 30, we use the combination formula which is nCr = n! / (r!(n-r)!). In this case, n = 30 and r = 5. Plugging these values into the formula, we get 30! / (5!(30-5)!) = 142,506 total combinations.
How do you do combinations in math?
nCr=n!/r!/(n-r)!
How many pints r in 8 gallons?
One gallon equals 8 pints.
7 pints equal how many gallons?
56 because there r 8 pints in a gallon,so 8 times 7 =56 it is that easy
How many pints make up eight quarts?
i think its 16 of then bcuz 8 qrts r 2 gallon
How many pints r in 2 gal?
That is 16 pints.
How many pints r in 5 quarts?
10 pints
How many guarts r in a gallon?
4 quarts in a gallon
How many pints r in 4 quarts?
1 quart = 2 pints 4 quarts = 2 x 4 = 8 pints
How many qt r in a 15 pints?
That is 3.5 quarts.
How many quarts and left over pints are in 15 pints?
1 qt = 2 pints 15 ÷ 2 = 7 r 1 → 15 pints = 7 quarts, 1 pint.
How many groups of 20 can you choose out of 23?
Combinations of r from n without replacement is c(n,r) = n!/(n-r)!r! c(n,r) = 23!/20!3! c(n,r) = 1771.
How many consonants are in you are a winner?
6 consonants: Y, R, W, N, N, R.
Prove that nCr plus nCr minus 1 equals n plus 1Cr?
nCr + nCr-1 = n!/[r!(n-r)!] + n!/[(r-1)!(n-r+1)!] = n!/[(r-1)!(n-r)!]*{1/r + 1/n-r+1} = n!/[(r-1)!(n-r)!]*{[(n-r+1) + r]/[r*(n-r+1)]} = n!/[(r-1)!(n-r)!]*{(n+1)/r*(n-r+1)]} = (n+1)!/[r!(n+1-r)!] = n+1Cr
