Q.In how many ways can the letters of the word "MOBILE" be arranged so that the vowels (O, I, E) always occupy the odd positions (1st, 3rd, 5th)?

EXPRESSION has 10 letters with $E,E$ and $S,S$ repeated (6 other distinct letters); split the 4-letter selections into 3 cases by how many repeated pairs are used, then count combinations and their arrangements separately.

Letters of EXPRESSION: $E,X,P,R,E,S,S,I,O,N$ — 10 letters total, with $E$ appearing twice, $S$ appearing twice, and $X,P,R,I,O,N$ each appearing once (6 distinct singles).

Combinations (selections of 4 letters), by case:

Case 1 — both pairs used ($E,E,S,S$): only $1$ way to choose this multiset.

Case 2 — exactly one pair used (either $EE$ or $SS$) plus 2 distinct singles from the 6: choose the pair in $2$ ways, choose 2 singles in $^6C_2=15$ ways: $2\times15=30$ combinations.

Case 3 — no pair used, all 4 letters distinct, chosen from the 8 distinct letter-types ($E,X,P,R,S,I,O,N$): $^8C_4=70$ combinations.

Total combinations $=1+30+70=101$.

Permutations (arrangements) for each case:

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