







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

From fae: 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 Answered by Janice Cotcher. 





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

From Anna: How can I prove that 2nCn is less than 4n, for all positive integers n? Answered by Penny Nom. 





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

From April: 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? Answered by Penny Nom. 





Successive coefficients in Pascal's Triangle 
20021227 

From Quincy: 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 Answered by Penny Nom and Walter Whiteley. 





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

From Tim: 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. Answered by Penny Nom. 





Pascal's Triangle 
20020402 

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





Lucas' theorem 
20011009 

From Tania: 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 Answered by Richard McIntosh. 





A dollar, quarter, dime, nickle and penny 
20010107 

From Sarah: 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... Answered by Penny Nom. 





649 
20000914 

From Steve: In our state lottery you must choose 6 numbers (149). How many different combinations are there? They can be in any order. Answered by Harley Weston. 





Binomial coefficients 
20000321 

From Howard Lutz: 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 Answered by Penny Nom. 





Multinomial coefficients 
19991203 

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





Cannonballs 
19990127 

From Roger King: How many cannonballs can be stacked in a triangular pyramid? Answered by Penny Nom. 

