SOLUTION: Find the coefficent of x^5y^5 in the expansion of (2x+3y)^10 thank you

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Question 63365: Find the coefficent of x^5y^5 in the expansion of (2x+3y)^10
thank you
Answer by venugopalramana(3286) About Me  (Show Source):
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Find the coefficent of x^5y^5 in the expansion of (2x+3y)^10
thank you
BINOMIL THEOREM FOR (A+B)^N GIVES THE GENERAL TERM AS
T (R+1) = [NCR]
HERE N=10
A=2X
B=3Y
R=5...SINCE WE WANT COEFFICIENT OF (X^5) * (Y^5)WHICH OCCURS WHEN R=5
HENCE..SUBSTITUTING AS ABOVE
T6= [10C5]
=[(10*9*8*7*6)/(5*4*3*2*1)][[X^5](3^5][Y^5]
COEFFICIENT OF (X^5) * (Y^5) IS
= 252*32*243 =1959552