Question

in how many different ways can the letters of the word TRADING be arranged such that the vowels always come together
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Answer 1

Answer:

1440

Step-by-step explanation:

T R A D I N G

There are total 7 letters

There are 2 vowels A and I

we will put these two vowels in a box and treat them as one element

then there will be 6 letters

so no. of ways will be 6! x 2! which is 1440

Answer 2

Answer:

The no. of ways of arranging the vowels always come  together is    TRDNG(AI) =  6!×2! = 1440 ways.

Step-by-step explanation:

Permutation:

• When the order of the arrangements counts, a permutation is a mathematical technique that establishes the total number of alternative arrangements in a collection.
• Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems.
• Permutations are frequently confused with combinations, a different mathematical concept.

Finding number of arrangements:

Given word is TRADING

   The word TRADING has 7 letters.

    It has 2 vowels A and I.

    So, now we have TRDNG(AI) = 6 letters(4+2)

    Treat the two vowels as 1 letter as show here TRDNG(AI).

    Internally vowels can be arranged in 2! ways.    

    The no. of ways of arranging the vowels always come

     together is TRDNG(AI) =  6!×2! = 1440 ways

Know more about Permutations:

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