How many different strings can be formed together
using the letters of the word “EQUATION” so that
I. How many of these are even?
II. How many of these are exactly divisible by 4?
Answers
Step-by-step explanation:
using the letters of the word “EQUATION” so that
I. How many of these are even?
II. How many of these are exactly divisible by 4?
I. The number of even-lettered strings is 62,216
II. The number of strings exactly divisible by 4 is 42,000
Given: Word is 'EQUATION'
To find:
I. Even-lettered strings are
II. Number of strings exactly divisible by 4 are
Solution:
I. We have the letters = E, Q, U, A, T, I, O, N
Number of letters in even-lettered strings = 2 or 4 or 6 or 8
No. of ways to form 2-letter words = 8 x 7 = 56
No. of ways to form 4-letter words = 8 x 7 x 6 x 5 = 1680
No. of ways to form 6-letter words = 8 x 7 x 6 x 5 x 4 x 3 = 1680 x 12=20,160
No. of ways to form 8-letter words = 8! = 40,320
⇒ Number of even lettered words = 56 + 1680 + 20,160 + 40,320 = 62,216
⇒ The number of even-lettered words = 62,216 Answer
II. Also, the number of strings exactly divisible by 4 = 4 or 8 lettered strings
As given earlier,
No. of ways to form 4-lettered words = 1680
No. of words to form 8-lettered words = 40,320
⇒ Total number of strings exactly divisible by 4 = 42,000 Answer
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