How many different arrangements are possible from alphabets of ENGLISH if the arrangements will start from N and end with G. (a) 5040 (b) 720 (c) 120 (d) 360
To find the number of different arrangements of the word "ENGLISH" where the arrangements start with "N" and end with "G," we can treat "N" and "G" as fixed positions and arrange the remaining letters.
Since "ENGLISH" has 7 letters in total, we have 5 remaining letters to arrange (E, I, L, S, H) between the fixed positions.
The number of ways to arrange these 5 letters is given by 5 factorial (5!), which is equal to 5 x 4 x 3 x 2 x 1 = 120.
Therefore, the correct answer is option (c) 120.
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Answers & Comments
Verified answer
Answer:
Total number of words formed without any restriction
=
7
!
Total number of words beginning with
I
=
6
!
Total number of words beginning with
B
=
6
!
Total number of words beginning with I and ends with
B
=
5
!
Therefore, required number of words
=
7
!
−
6
!
−
6
!
+
5
!
=
5040
−
2
×
720
+
120
=
3720
Answer:
To find the number of different arrangements of the word "ENGLISH" where the arrangements start with "N" and end with "G," we can treat "N" and "G" as fixed positions and arrange the remaining letters.
Since "ENGLISH" has 7 letters in total, we have 5 remaining letters to arrange (E, I, L, S, H) between the fixed positions.
The number of ways to arrange these 5 letters is given by 5 factorial (5!), which is equal to 5 x 4 x 3 x 2 x 1 = 120.
Therefore, the correct answer is option (c) 120.
Great job with the question! If you have any more, feel free to ask.