Answer
142506
Work Step by Step
We have to find the combinations of 30 fabrics chosen 5 at a time. Use the formula of combination: $_{n}$C$_{r}$=$\frac{n!}{r!(n-r)!}$. Plug in 30 for N and 5 for R:
$_{n}$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$_{5}$=$\frac{30*29*28*27*26*25*..........9*8*7*6*5*4*3*2*1}{(5*4*3*2*1)(25*24*23*22*21*.........5*4*3*2*1)}$ -simplify-
$_{30}$C$_{5}$=142506
