Respuesta :

guesst555
AARDVARK has 3 A's, 2 R's, 1 D, 1 V, and 1 K. If all three A's have to be together, then treat them as one letter. So there are a total of 6 "letters" to arrange. There would be 6! ways to arrange them if the "letters" were all different, but you have to keep in mind that there are 2 R's which are the same, so you need to divide out the number of ways to arrange the R's if they were different, which is 2!. 

So, in total, there are 6!/2! = 360 ways to arrange the letters in AARDVARK if all three A's must be consecutive.

The number of different strings that can be made from the letters in aardvark, using all the letters, if all three 'a's must be consecutive is 360

What is the number of permutations in which n things can be arranged such that some groups are identical?

Suppose there are n items.

Suppose we have [tex]i_1, i_2, ..., i_k[/tex] sized groups of identical items.

Then the permutations of their arrangements(all distinct) is given as

[tex]\dfrac{n!}{i_1! \times i_2! \times ... \times i_k!}[/tex]

For this case, we have the letter "aardvark" for which we've to find the number of its arrangements such that all three 'a's remain together.

Take them as a packet. Pack them and consider them as a single unit.

Then you have 1 packet of 'a's, 2 'r's, 1 d, 1 v and 1 k.

Thus, total 6 items, or say  n = 6

Out of them, there is 2 sized group of 'r' which is identical.

Thus, the permutations of their arrangements(all distinct) is given as:

[tex]\dfrac{6!}{2!} = 6\times 5 \times 4 \times 3 =360[/tex]

Thus, the number of different strings that can be made from the letters in aardvark, using all the letters, if all three 'a's must be consecutive is 360

Learn more about permutations here:

https://brainly.com/question/6743939

Otras preguntas

Q&A Education