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QJEEM23Ma8cf4: JEE Main 2023 Mathematics - Class 11 JEEM23Ma8cf4 Solution: The number of arrangements of the letters of the word…

The number of arrangements of the letters of the word "INDEPENDENCE" in which all the vowels always occur together is :

Step-by-Step Verified Solution

In the given word,

vowels are : I, E, E, E, E

Consonants are : N, D, P, N, D, N, C

So, number of words

=\frac{8 !}{3 ! 2 !} \times \frac{5 !}{4 !}

=\frac{8 \times 7 \times 6 \times 5 \times 4}{2} \times 5=16800

Concept :

Out of

n

objects, if

r

things are same, so number of ways

=\frac{n !}{r !}