number of 4 letter words formed former barrack
Answers
Answered by
18
hey mate
How many 4-letter words can be formed using the letters of the word BARRACK?
Still have a question? Ask your own!
What is your question?
6 ANSWERS
Partha Chattopadhyay (পার্থ চট্টোপাধ্যায়), former Civil Servant & former lecturer in a college
Answered May 10, 2018 · Author has 1.5k answers and 882.3k answer views
There are 5 distinct letters (B,A,R,C & K) in the word BARRACK with A &R being repeated twice. To form 4-lettered words, there will be 4 situations viz. (i) all 4 different (ii) 2 are different and other 2 are A's (iii) 2 are different and other 2 are R's (iv) 2 are A's and other 2 are R's.
Case (i): The first letter out of 5 can be chosen in 5 ways. The second letter can be chosen out of remaining 4 in 4 ways. Again, the third letter can be chosen out of remaining 3 in 3 ways and lastly the fourth letter can be chosen out of remaining 2 in 2 ways. Hence, total arrangements of 4 lettered words with no repetition is 5*4*3*2 = 120.
Case (ii): Here, 2 letters are different and other 2 letters are both A . But, 2 letters can be chosen out of 4 ( B,R,C & K) in C(4,2)=6C(4,2)=6ways. Again, this 4-lettered word with 2 A 's can be arranged in 4!/2!=124!/2!=12 ways. So, total arrangement is 6*12 =72.
Case (iii) : Similarly, when 2 letters are different and 2 letters are both R , the total arrangement is also 72.
Case (iv) : Here, 2 letters are both R and remaining 2 letters are both A and hence, the total arrangement is 4!/(2!∗2!)=6.4!/(2!∗2!)=6.
So, the total number of 4 lettered words is 120+72+72+6 = 270
if it help u
mark me brainlist
How many 4-letter words can be formed using the letters of the word BARRACK?
Still have a question? Ask your own!
What is your question?
6 ANSWERS
Partha Chattopadhyay (পার্থ চট্টোপাধ্যায়), former Civil Servant & former lecturer in a college
Answered May 10, 2018 · Author has 1.5k answers and 882.3k answer views
There are 5 distinct letters (B,A,R,C & K) in the word BARRACK with A &R being repeated twice. To form 4-lettered words, there will be 4 situations viz. (i) all 4 different (ii) 2 are different and other 2 are A's (iii) 2 are different and other 2 are R's (iv) 2 are A's and other 2 are R's.
Case (i): The first letter out of 5 can be chosen in 5 ways. The second letter can be chosen out of remaining 4 in 4 ways. Again, the third letter can be chosen out of remaining 3 in 3 ways and lastly the fourth letter can be chosen out of remaining 2 in 2 ways. Hence, total arrangements of 4 lettered words with no repetition is 5*4*3*2 = 120.
Case (ii): Here, 2 letters are different and other 2 letters are both A . But, 2 letters can be chosen out of 4 ( B,R,C & K) in C(4,2)=6C(4,2)=6ways. Again, this 4-lettered word with 2 A 's can be arranged in 4!/2!=124!/2!=12 ways. So, total arrangement is 6*12 =72.
Case (iii) : Similarly, when 2 letters are different and 2 letters are both R , the total arrangement is also 72.
Case (iv) : Here, 2 letters are both R and remaining 2 letters are both A and hence, the total arrangement is 4!/(2!∗2!)=6.4!/(2!∗2!)=6.
So, the total number of 4 lettered words is 120+72+72+6 = 270
if it help u
mark me brainlist
Answered by
3
Step-by-step explanation:
This is the Answer.
hope this will help you.
Attachments:
Similar questions