Find the number of distinguishable permutations of:2 Bs, 3 Hs, and 6 Os(B, B, H, H, H, O, O, O, O, O, O)If you could explain how / the formula, that would be great

1 answer
Question:

Find the number of distinguishable permutations of:
2 Bs, 3 Hs, and 6 Os
(B, B, H, H, H, O, O, O, O, O, O)
If you could explain how / the formula, that would be great

Answers

There are a total of 2 + 3 + 6 = 11 letters, which gives rise to 11! possible permutations.Consider one such permutation:BBHHHOOOOOOI write one of the Bs in the bold for emphasis. This permutation is not distinguishable (but for the temporary boldface) fromBBHHHOOOOOOwhich is to say they both count as the same permutation. To avoid counting this twice, you would divide the total number of permutations by the number of ways you can permute the identical character. In the case of Bs, this can be done in 2! = 2 ways.Similarly, the 3 Hs can be rearranged in 3! = 6 ways, and the 6 Os can be rearranged in 6! = 720 ways.Then the total number of distinguishable permutations is11! / (2! • 3! • 6!) = 4620As a formula: given a word of length [tex]N[/tex] with [tex]n[/tex] different characters that respectively occur [tex]k_n[/tex] times, the total number of distinct permutations is[tex]\dfrac{N!}{k_1! k_2! k_3! \cdots k_n!}[/tex]where [tex]k_1+k_2+k_3+\cdots+k_n=N[/tex].Try this with some simple examples:• GREECEThis has length 6, with E occurring three times, and every other letter occurs once. The total number of distinct permutations of GREECE is6! / (1! • 1! • 1! • 3!) = 120• BANANAThis also has length 6, with B occurring once, N twice, and A three times, so the total number of distinct permutations of BANANA is6! / (1! • 2! • 3!) = 60• STATISTICALLYThis has length 13, with one each of C and Y; two each of S, A, I, L; and three Ts. Then the number of distinct permutations is13! / (1! • 1! • 2! • 2! • 2! • 2! • 3!) = 64,864,800

Similar Solved Questions

2 answers

How can i kin bakugo and toga

How can i kin bakugo and toga...
2 answers

A snake slithers along the ground. Which force works against the snake's forward motion? A. magnetism B. friction C. spring D. gravity

A snake slithers along the ground. Which force works against the snake's forward motion? A. magnetism B. friction C. spring D. gravity...
1 answer

Sean has 5.50 in dimes and quarters. he has 8 more quarters than dimes. how many quarters does he have

Sean has 5.50 in dimes and quarters. he has 8 more quarters than dimes. how many quarters does he have...
1 answer

If 2cups of cranberry juice and 3gallons of punch make punch using the same recipe what is the amount of cranberry juice needed for 1 gallon punch

If 2cups of cranberry juice and 3gallons of punch make punch using the same recipe what is the amount of cranberry juice needed for 1 gallon punch...
1 answer

How might an ecologist test whether a species is occupying its complete fundamental niche or only a portion of it? how might an ecologist test whether a species is occupying its complete fundamental niche or only a portion of it?

How might an ecologist test whether a species is occupying its complete fundamental niche or only a portion of it? how might an ecologist test whether a species is occupying its complete fundamental niche or only a portion of it?...
1 answer

In order to lure new customers to a credit card

in order to lure new customers to a credit card...
2 answers

Which quadrilateral has equal diagonalsA.parallelogram B.rhombus C.trapezoid D.rectangleE.none​

which quadrilateral has equal diagonalsA.parallelogram B.rhombus C.trapezoid D.rectangleE.none​...
1 answer

Enter the area of the triangle in square units rounded to the nearest 10th PLS PLS PLS HELP

enter the area of the triangle in square units rounded to the nearest 10th PLS PLS PLS HELP...
1 answer

Please help me!!!!!!!!!!!!

please help me!!!!!!!!!!!!...
1 answer

See question in image and show workings​Note : 1 nautical mile = 1.86km

See question in image and show workings​Note : 1 nautical mile = 1.86km...
1 answer

Solve for: 1/2 divided by 7 1/2=

Solve for: 1/2 divided by 7 1/2=...
1 answer

Write a linear equation with the given information. Passing through (2, 3) and PARALLEL to y = x - 4

Write a linear equation with the given information. Passing through (2, 3) and PARALLEL to y = x - 4...
2 answers

The energy needs of a human population are NOT affected by which of the following factors? A standard of living B location of energy sources C use of technology D amount of industry

The energy needs of a human population are NOT affected by which of the following factors? A standard of living B location of energy sources C use of technology D amount of industry...
1 answer

As countries move from agricultural to industrial to services economies, birthrates increase. True False

As countries move from agricultural to industrial to services economies, birthrates increase. True False...
2 answers

Help me please someone

help me please someone...
1 answer

Why was Captain Henry Wirz, the officer at Andersonville Prison, executed after the war? A. He refused to allow a prisoner swap. B. He made the prisoners work in the fields and factories surrounding the prison. C. He used the prison to keep POWs from returning to the war and continuing the fighting. D. He was charged with cruelty to the prisoners-sickness, poor conditions, and few supplies caused over 13,000 POWs to die there.

Why was Captain Henry Wirz, the officer at Andersonville Prison, executed after the war? A. He refused to allow a prisoner swap. B. He made the prisoners work in the fields and factories surrounding the prison. C. He used the prison to keep POWs from returning to the war and continuing the figh...
1 answer

What did the women's march on versailles accomplish?

What did the women's march on versailles accomplish?...
1 answer

List three ways in which the Nazi party was able to gain power despite not having a majority of Germans support​

list three ways in which the Nazi party was able to gain power despite not having a majority of Germans support​...
1 answer

PLEASE ANSWER THIS ILL GIVE BRAINLIEST

PLEASE ANSWER THIS ILL GIVE BRAINLIEST...

-- 0.009991--