use a calculator to evaluate the expression.\n$_{29}c_{17}$\n$_{29}c_{17}=\\square$
use a calculator to evaluate the expression.\n$_{29}c_{17}$\n$_{29}c_{17}=\\square$
Answer
Explanation:
Step1: Recall the combination formula
The formula for combinations is ( nC_r=\frac{n!}{r!(n - r)!} ). For ( {29}C{17} ), we can also use the property ( nC_r = nC{n - r} ), so ( {29}C{17}={29}C{29 - 17}={29}C{12} ), which might be easier to calculate, but we can directly use a calculator.
Step2: Use calculator to compute
Using a calculator (either a scientific calculator or a calculator with combination function), we input ( n = 29 ), ( r=17 ) for the combination function ( _nC_r ). The result of ( {29}C{17} ) is calculated as follows: First, calculate the factorials (or use the combination formula in the calculator). The value of ( {29}C{17}=\frac{29!}{17!(29 - 17)!}=\frac{29!}{17!×12!} ). Calculating this (either by expanding factorials or using calculator shortcuts), we get ( {29}C{17}=10015005 ).
Answer:
( 10015005 )