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

Answer:

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

                            85,765,680

Step-by-step 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:

$=\dfrac{17!}{6!\times 5!\times 2!\times 4!}\\\\\\=\dfrac{17\times 16\times 15\times 14\times 13\times 12\times 11\times 10\times 9\times 8\times 7\times 6!}{6!\times 5!\times 2!\times 4!}\\\\=\dfrac{17\times 16\times 15\times 14\times 13\times 12\times 11\times 10\times 9\times 8\times 7}{ 5!\times 2!\times 4!}$

which on solving gives us: 85,765,680

Hence, the number of ways of doing so is:

                              85,765,680