







n choose r equals n1 choose r plus n1 choose r  1 
20080714 

fae pose la question : Prove that
( n ) = ( n – 1) + ( n  1 )
( r ) ( r ) (r1)
NOTE: the ( ) should be one for n taken r and so on. but there is no one big ( ) that will cater two lines Janice Cotcher lui répond. 





Prove that 2nCn is less than 4n, for all positive integers n? 
20061001 

Anna pose la question : How can I prove that 2nCn is less than 4n, for all positive integers n? Penny Nom lui répond. 





What are the 3rd and 4th terms of (2xy)^7? 
20060618 

April pose la question : What are the 3rd and 4th terms of this sequence: (2xy)^{7}?
I'm having an issue with this...is there any easier way to get it without completely factoring the whoooole thing out? Penny Nom lui répond. 





Successive coefficients in Pascal's Triangle 
20021227 

Quincy pose la question : There is a formula connecting any (k+1) successive coefficients in the nth row of the Pascal Triangle with a coefficient in the (n+k)th row. Find this formula Penny Nom and Walter Whiteley lui répond. 





Successive coefficients in the nth row of Pascal's Triangle 
20020610 

Tim pose la question : There is a formula connecting any (k+1) successive coefficients in the nth row of Pascal's Triangle with a coefficient in the (n+k)th row. find this formula. Penny Nom lui répond. 





Pascal's Triangle 
20020402 

Brian pose la question : It's about (a+b)^{x}. I remember there a triangle with numbers to remember for a faster solution. Can you please teach me? Penny Nom lui répond. 





Lucas' theorem 
20011009 

Tania pose la question : How could I demonstrate: nCp is congruent to floor(n/p) (modulo p)? where rCk is a binomial coefficient, rCk = r(r1)...(rk+1)/k(k1)...1, and p is a prime number Richard McIntosh lui répond. 





A dollar, quarter, dime, nickle and penny 
20010107 

Sarah pose la question : Arnold has a dollar coin, one dime, one quarter, one nickel, and a penny. The number of different sums of money that can be formed using three coins is... Penny Nom lui répond. 





649 
20000914 

Steve pose la question : In our state lottery you must choose 6 numbers (149). How many different combinations are there? They can be in any order. Harley Weston lui répond. 





Binomial coefficients 
20000321 

Howard Lutz pose la question : How do you find each successive numerical term in this equation y+dy=(x+dx)^{5} =x^{5}+5*x^{4}dx+10*x^{3}(dx)^{2}+10*x^^{2}(dx)^{3}+5*x(dx)^{4}+(dx)^{5} I would appreciate an explanation of the method to find the numeric coefficient in a binomial expansion Penny Nom lui répond. 





Multinomial coefficients 
19991203 

Suraj Das pose la question : Is there a formula for the expansion of (a+b+c) to the nth power? Does it have to do with Pascal's triangle? Penny Nom lui répond. 





Cannonballs 
19990127 

Roger King pose la question : How many cannonballs can be stacked in a triangular pyramid? Penny Nom lui répond. 

