Question

An electronic salesperson carries 6 identical amplifier tubes, 5 identical rectifiers, 2 identical condensers, and 4 identical relays. In how many different ways can these parts be arranged in a row?

Answer 1

No of arrangement = (6+5+2+4)! / (6! * 5! * 2! * 4!) = 17! / (6! * 5! * 2! * 4!) = (17 * 16 * 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (6 * 5 * 4 * 3 * 2 * 1 * 5 * 4 * 3 * 2 * 1 * 2 * 1 * 4 * 3 * 2 * 1) = 85,765,680

Answer 2

The number of ways of arranging these items in a row is:

85,765,680

Explanation:

It is given that:

An electronic salesperson carries 6 identical amplifier tubes, 5 identical rectifiers, 2 identical condensers, and 4 identical relays.

Hence, the total number of items are:

17 ( since 6+5+2+4=17)

Hence, the number of ways it could be arranged in a row is calculated as:

`=(17!)/(6!* 5!* 2!* 4!)\\\\\\=(17* 16* 15* 14* 13* 12* 11* 10* 9* 8* 7* 6!)/(6!* 5!* 2!* 4!)\\\\=(17* 16* 15* 14* 13* 12* 11* 10* 9* 8* 7)/( 5!* 2!* 4!)`

which on solving gives us: 85,765,680

Hence, the number of ways of doing so is:

85,765,680