Find the numbers of arrangement that can be made out of the letters of the following words :- (a) COLLEGE , (b) MATHEMATICS. Chp :- permutation plz answer.
Answers
⬇⬇⬇⬇⬇⬇⬇⬇
✒Given , (a) COLLEGE
There are 7 letters in the word COLLEGE
Again ,
L ➡ 2
E ➡ 2
So total permutation
= 7! / 2!×2!
= 7×6×5×4×3×2×1/ 2×1×2×1
= 7×6×5×3×2
= 1260
So , the word COLLEGE can be arranged in 1260 ways .
✒(b)MATHEMATICS
There are 11 letters in the word MATHEMATICS
Where
M ➡ 2
T ➡ 2
A ➡ 2
So total permutations
=11!/ 2!×2!×2!
= 11×10×9×8×7×6×5×4×3×2×1/ 2×2×2
= 11×10×9×8×7×6×5×3
=110×81×7×30×3
= 110×81×7×90
= 4989600
Therefore the letters of the word MATHEMATICS can be arranged in 4989600 ways .
HOPE WILL HELP ☺☺
✔✔✔✔✔✔✔
Answer:
(a) The number of arrangements that can be made using the letters COLLEGE is 1260.
(b) The number of arrangements that can be made using the letters MATHEMATICS is 4,989,600.
Step-by-step explanation:
Given,
The words,
(a) COLLEGE
(b) MATHEMATICS
To find,
The number of ways to arrange the words COLLEGE and MATHEMATICS.
Calculation,
(a) COLLEGE
In the word COLLEGE, there are 7 letters in total so there are 7 empty blanks that can be filled with the help of the word COLLEGE.
i.e. _ _ _ _ _ _ _
So, in the first blank there are 7 possibilities, in the second blank there are 6 possibilities, so on up to in the last blank there is 1 possibility, but as in the word COLLEGE, there are 2 repetitive letters i.e. the letter 'L', and 'E' two times.
Hence, the no. of possibilities are:
7!/(2!)(2!)
= 5040/4
= 1260
Therefore, the number of arrangements that can be made using the letters COLLEGE is 1260.
(b) MATHEMATICS
In the word MATHEMATICS, there are 11 letters in total so there are 11 empty blanks that can be filled with the help of the word MATHEMATICS.
i.e. _ _ _ _ _ _ _ _ _ _ _
So, in the first blank there are 11 possibilities, in the second blank there are 10 possibilities, so on up to in the last blank there is 1 possibility, but as in the word MATHEMATICS, there are 3 repetitive letters i.e. the letter 'M', 'A' and 'T' two times.
Hence, the no. of possibilities are:
11!/(2!)(2!)(2!)
= 39,916,800/8
= 4,989,600
Therefore, the number of arrangements that can be made using the letters MATHEMATICS is 4,989,600.
#SPJ2