How many words can be formed from the letter of the word ENGLISH ?How many of these do not being with E?How not end with H?
Answers
Answer:
5040
Step-by-step explanation:
There are 7 letters in the word ENGLISH. Permutation of 7 letters in 7 places can be done in P(7,7) ways. Formula: Number of permutations of n distinct objects among r different places, where repetition is not allowed, is P(n,r) = n!/(n-r)! Therefore, a permutation of 7 different objects in 7 places is P(7,7) 7 ! ( 7 − 7 ) ! 7!(7−7)! = 7 ! 0 ! 7!0! = 5040 1 50401 = 5040. Hence, the total number of permutations is P 5040. To find a number of words starting with E and ending with I, let us consider their position which is 1st and 7th . --------- E ? ? ? ? ? 1 The rest 5 letters are to be arranged in 5 places which can be done in P (5,5) Formula: Number of permutations of n distinct objects among r different places, where repetition is not allowed, is P(n,r) = n!/(n-r)! Therefore, a permutation of 5 different objects in 5 places is P(5,5) = 5 ! ( 5 − 5 ) ! 5!(5−5)! = 5 ! 0 ! 5!0! = 120 1 1201 = 120. Therefore, there are 120 words starting with E and ending with I.Read more on Sarthaks.com - https://www.sarthaks.com/1164559/find-the-number-permutations-the-letters-the-word-english-how-many-these-begin-with-and-with