Question

# In the word ‘ALLAHABAD’ how many of these vowels occupy the even positions?

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Hint:Find out the number of vowels and their places and apply Factorial.
First count the vowels in the given word. Later place the vowels as said in the question and find the permutation.

So, these four places can be occupied by 4 vowels in $$\dfrac{{4!}}{{4!}}$$ = 1 way;
These can be arranged in $$\dfrac{{5!}}{{2!}}$$ ways;
Total no. of words in which vowels occupy the even places = $$\dfrac{{5!}}{{2!}}$$
$$n! = n(n - 1)!$$
= $$\dfrac{{5 \times 4 \times 3 \times 2 \times 1}}{{2 \times 1}}$$= 160