Question

in how many way can the letters of the word OPPORTUNITY can be arranged so that two O's always occur together?

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Answer 1

Answer:

(i)

there are 5!5! letters spelled "salno" and we put the remaining o in the 4 space in the word spelling "salono." we need to divide by 2.

5!∗4/2=240

(ii)

6 ways to orient the consonants, and 3 ways to orient the vowels (again that double o thing). We could start with a vowel, or we could start with a consonant.

6∗3∗2=36

In the word “FAILURE’ there are 4 odd position for letters and three even positions.

Now we have 3 consonants and 4 places. Hence they can be arranged in 4P3=4∗3∗2=244P3=4∗3∗2=24 ways

Remaining must be occupied by vowels in 4!ways=244!ways=24

Hence number of ways =24∗24=576=24∗24=576