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First count the vowels in the given word. Later place the vowels as said in the question and find the permutation.

Total no. of vowels in the word ‘ALLAHABAD’ = 4 (all a’s);

Even places of vowels = 2nd, 4th, 6th and 8th;

So, these four places can be occupied by 4 vowels in $$\dfrac{{4!}}{{4!}}$$ = 1 way;

Now, 5 places are left in which 5 letters (two are same and three different);

Same letter is L and two different letters are B,H and D.

These can be arranged in $$\dfrac{{5!}}{{2!}}$$ ways;

Total no. of words in which vowels occupy the even places = $$\dfrac{{5!}}{{2!}}$$

As we know,

$$n! = n(n - 1)!$$

= $$\dfrac{{5 \times 4 \times 3 \times 2 \times 1}}{{2 \times 1}}$$= 160

Permutation is the act of arranging objects. Combination is the selection of a few items from the total number of items.