How do you evaluate #((8), (7))# using Pascal's triangle?

1 Answer
Feb 12, 2018

Answer:

#((8),(7))=8#

Explanation:

When I have a sum of the sort #((n),(k)),# the number #n# corresponds to the row number of Pascal's Triangle, and #k# corresponds to the column number of that row, where the first column has the value #k=0#.

#((n),(k))# is typically read "#n# choose #k#." There is a formula to find it:

#((n),(k))=(n!)/(k!(n-k)!)#, where #!# is the factorial function.

So inputting the values for #n# and #k# in this situation gives:

#(8!)/(7!(8-7)!)#

#(8*cancel(7!))/(cancel(7!)*1!)#

#=8#

It is important to note that #((n),(n-1))=n#.

We can also use Pascal's Triangle:

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Remember, the first row and column are given by #n=0# and #k=0# respectively.

Going to the eigth row and the seventh column gives us the same number, #8#.