Question

How many distinguishable ways can the letters of the word millimicron be arranged in order?

Answer 1

total no. of letters = 11

millimicron

dissecting will give us:

 

no. of m = 2, no. of i = 3, no. of l = 2, no. of c = 1, no. of n =1, no. of r = 1, no. of o = 1

 

 we are going to compute this by using permutation

total no. of ways to arrangement = 11!/ [ 2!* 3! * 2! * 1! *1! *1! *1!]

= 39,916,800/ 24

= 1,663,200 is the answer

Answer 2

There are 1663200 distinguishable ways that the letters of the word millimicron can be arranged in order.

Further explanation

The probability of an event is defined as the possibility of an event occurring against sample space.

$\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }$

Permutation ( Arrangement )

Permutation is the number of ways to arrange objects.

$\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }$

Combination ( Selection )

Combination is the number of ways to select objects.

$\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }$

Let us tackle the problem.

This problem is about Permutation with same objects.

The word "millimicron" consists of :

2 letters "m"

3 letters "i"

2 letter "l"

1 letter "c"

1 letter "r"

1 letter "o"

1 letter "n"

These total of 11 letters can be arranged as much $11!$ ways

Because there are 2 letters "m" , 3 letters "i" , 2 letter "l" , then :

$\text{Total Distinguishable Arrangement} = \frac{11!}{2! ~ 3! ~ 2!}$

$\text{Total Distinguishable Arrangement} = 1663200$

Learn more

• Different Birthdays : https://brainly.com/question/7567074
• Dependent or Independent Events : https://brainly.com/question/12029535
• Mutually exclusive : https://brainly.com/question/3464581

Answer details

Grade: High School

Subject: Mathematics

Chapter: Probability

Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation