11. Solve the problem. many different 4-letter codes are there if only the lette
ID: 2912676 • Letter: 1
Question
11. Solve the problem. many different 4-letter codes are there if only the letters A, B, C, D, E, F, G, H, and I can be used and no letter can be used more than once? a. 126 b. 3024 c. 6561 d. 4 2. Solve the problem. ow many different license plates can be made using 2 letters followed by 3 digits selected from the digits 0 through 9, if neither letters nor digits may be repeated? a. 468,000 b. 327,600 c. 676,000 d. 39,000 Solve the problem. rodes can be formed using the letters A, B, C, D, E, and F? Repeated letters are aExplanation / Answer
Answer:
(11)
Given that , there are nine distinct letters of the alphabets . To find number of different four letter codes where no letters are repeated . Now we assign four places for each of the letters of the four letter word.
For the first place we can have 9 letters , as one place has been filled with a letter ,we cannot repeat that letter and so for the second place we have 8 letters which we can fill ,similarly for the third place as two of the 9 letters have been filled we are left with 7 letters , and fourth place we have 6 letters which we can fill in the fouth place. So in total we have a possible combination of 9x8x7x6=3024, different four letter codes where no letters are repeated .
Therefore answer is (b).
(12)
Here total number of distinct letters=26,
Out this 26 letters we have to choose 2 letters which are non-repititive, which can be done in 26x25 ways.
Total number of distinct digits=10,
out of these 10 digits we are to select three digits which are non-repititive, which can be done in 10x9x8 ways.
Now, total number of ways in which two letters can be selected followed by selection of three digits from 0 to9 where no alphabets or digits are repeated is given by 26x25x10x9x8=468000.
Therefore answer is (a).
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.