It's urgent plz

Question

Consider the name as MARIAHOSSAIN and Roll number as 21101164.

1.Find the total number of arrangements from the letters of your name taken all at a time without changing the the positions of vowels and consonants.

2.find the total number of three digit numbers possible from the digits of your roll number.

3.Consider a license plate of 8 letters long.First 4 letters include only alphabets and the second 4 letters include digits only. How many license plate can be made in this way if the Alphabet comes from your name and digits come from your roll number?

Answer 1

"Divide and Conquer." You can break a big problem down into little pieces, solve each piece, and then extract information from these solutions to solve your big problem.

1.Find the total number of arrangements from the letters of your name taken all at a time without changing the the positions of vowels and consonants. Is this part of the question copied correctly? Is it asking about changing the positions of vowels AND consonants or is it a two-part question, first vowels, second consonants. If you do not change the position of both vowels and consonants, what rearrangements can happen?

2.find the total number of three digit numbers possible from the digits of your roll number. "total number of 3 digit numbers" signals that this is a permutation problem, i.e., order matters. First, what are the unique digits in your 8 digit roll number?21101164 has unique digits [0,1,2,4,6]. 5 unique digits. This part of the problem becomes a 5P3 permutation problem. N!/(N-r)! will give you the number of 3 digits numbers possible from the digits in the roll call number. You can check your work with the PERMUT function in excel.

3.Consider a license plate of 8 letters long.First 4 letters include only alphabets and the second 4 letters include digits only. How many license plate can be made in this way if the Alphabet comes from your name and digits come from your roll number? If you've worked your way through part 2 above, you know how to do the first two parts of this question. part 1, determine the number of unique 4-letter permutations than can come from the unique letters in your name. part 2, determine the number of unique 4 digit permutations that can come from the 5 unique digits in the roll call number. for part 3, simplify multiply the answers from part 1 and part 2. Each of your letter permutations can combine with each of your number permutations. For instance, if you had 3 letter permutations and 4 number permutations, you could get 12 arrangements out of this.

Best of luck. Feel free to check back in.