Answer to Question #95964 in Combinatorics | Number Theory for Black Gold

Question

A researcher wishes to study railroad accidents he wishes to say like three rows from 10 class one railroads to rail road from six close to real world and one rail road for five class III real rose how many different possibilities are there for his study

Answer 1

The number of ways of selecting 3 railroads from 10 Class I railroads is

$$\binom{10}{3}={10! \over 3!(10-3)!}={10\cdot9\cdot8 \over 1\cdot2\cdot3}=120$$

The number of ways of selecting 1 railroad from 6 Class II railroads is

$$\binom{6}{1}={6! \over 1!(6-1)!}=6$$

The number of ways of selecting 1 railroad from 5 Class III railroads is

$$\binom{5}{1}={5! \over 1!(5-1)!}=5$$

Using the multiplication rule we have

$$120\cdot6\cdot5=3600$$

There are 3600 different possibilities for his study.