Question

< > o III Counting rangements of objects that are not al Alessis hagin 13 sweaterson and. He has 3 gray sweaters 4 green sweaters, and white waters. In how many distinct orders as the Sweaters be arranged to waters of the same color are consideredentical (not distinct)? 5 2 N C

Answer 1

The number of distinct arrangements or orders that are possible of 'n' objects, such that r₁ objects are identical of one kind, r₂ objects are identical of another kind, and r₃ objects are identical of a third kind is given by the formula

Here, there are a total of 13 objects, so $n=13$ ,

There are 3 identical gray sweaters, so $r_1=3$

There are 4 identical green sweaters, so $r_2=4$

There are 6 identical white sweaters, so $r_3=6$

Applying the formula, number of distinct orders possible

$n!/r_1!r_2!r_3!=13!/3!4!6!$

We know, any factorial of the form can be written as .

So,13! can be further simplified as $13!=13*12*11*10*9*8*7*6!$

Simplifying the expression, we get

$=(13*12*11*10*9*8*7)/(6*24)$

$=8648640/144$

$=60060ways$

Hence, the sweaters can be arranged in 60060 ways.