Distribution into Bins
\[ \large A \times B \times C \times D \times E \times F = 7 \times 10^7 \]
Determine the number of ordered solutions for integers \(A,B,C,D,E,F\) such that they satisfy the equation above.
by
Pi Han Goh
How many 6-digit numbers can be formed using exactly 4 different digits?
by
Sandeep Bhardwaj
\(10,10,10\)
\(10,10,5\)
\(10,10,1\)
\(10,5,5\) ... etc.
Find the number of divisible sequences of length 5 starting from the number 360.
by
jatin yadav
Seven identical eggs are being put into a \(15 \times 1 \) egg box. However no more than two eggs can be put in a row. For example, one possible arrangement is E-E----EE-E--EE.
How many possible arrangements are there for the eggs?
Note: The egg box always stays in the same orientation so reflections count.
by
Michael Ng
Let \( p(n) \) be the number of partitions of \( n\). Let \(q(n) \) be the number of partitions of \( 2n \) into exactly \(n \) parts. For example, \(q(3) = 3 \) because \[ 6 = 4+1+1 = 3+2+1 = 2+2+2. \] Compute \( p(12)-q(12). \)
Definition: A partition of an integer is an expression of the integer as a sum of one or more positive integers, called parts. Two expressions consisting of the same parts written in a different order are considered the same partition ("order does not matter").
by
Patrick Corn