Question

Find the number of ways so that letters of the word HISTORY can be arranged as Y and T are together

Answer 1

Total number of ways in which the letters of the word HISTORY can be arranged=1440

Step-by-step explanation:

Given word:HISTORY

Total letters in the given word=7

When TY comes together then TY act as a single letter.

Therefore, total letters in the word=6

Let TY=P

Number of ways in which the word HISPOR can be arranged=6!

Number of ways in which TY can be arranged=2!

Therefore, total number of ways in which the letters of the word HISTORY can be arranged=$2!\times 6!=2\times 1\times 6\times 5\times 4\times 3\times 2\times 1$

By using the formula

$n!=n(n-1)(n-2)...2\times 1$

Total number of ways in which the letters of the word HISTORY can be arranged=1440

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