Answer
142506 different 5-fabrics
Work Step by Step
Use the formula of combination: $_{n}$C$_{r}$=$\frac{n!}{r!(n-r)!}$. Plug in 30 for N and 5 for R because we have to find the combinations of 30 fabrics chosen 5 at a time
$_{n}$C$_{r}$=$\frac{n!}{r!(n-r)!}$
$_{30}$C$_{5}$=$\frac{30!}{5!(30-5)!}$ -simplify like terms-
$_{30}$C$_{5}$=$\frac{30!}{5! (25!)}$ -write using factorial-
$_{30}$C$_{5}$=$\frac{30*29*28*27*26*25*24*23*22*21*20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1}{(5*4*3*2*1)(25*24*23*22*21*20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1)}$ -simplify-
$_{30}$C$_{5}$=142506
There are 142506 different 5-fabrics
