Topic: binomial coefficients list of topics
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12 items are filed under this topic.

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	n choose r equals n-1 choose r plus n-1 choose r - 1		2008-07-14
		From fae: Prove that ( n ) = ( n – 1) + ( n - 1 ) ( r )         ( r )        (r-1) 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?		2006-10-01
		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 (2x-y)^7?		2006-06-18
		From April: What are the 3rd and 4th terms of this sequence: (2x-y)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		2002-12-27
		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		2002-06-10
		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		2002-04-02
		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		2001-10-09
		From Tania: How could I demonstrate: nCp is congruent to floor(n/p) (modulo p)? where rCk is a binomial coefficient, rCk = r(r-1)...(r-k+1)/k(k-1)...1, and p is a prime number Answered by Richard McIntosh.
	A dollar, quarter, dime, nickle and penny		2001-01-07
		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.
	6-49		2000-09-14
		From Steve: In our state lottery you must choose 6 numbers (1-49). How many different combinations are there? They can be in any order. Answered by Harley Weston.
	Binomial coefficients		2000-03-21
		From Howard Lutz: How do you find each successive numerical term in this equation y+dy=(x+dx)5 =x5+5*x4dx+10*x3(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		1999-12-03
		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		1999-01-27
		From Roger King: How many cannonballs can be stacked in a triangular pyramid? Answered by Penny Nom.

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