i) No O's so there's 5 letters and we must pick 4 - 5C4

ii) 8 O's so 8C4

iii) We pick the 3 L's through 3C3 then 1 letter from the others so 10C1, 3C3 x 10C1

iv) Pick one O first, so 8C1, now pick the other 3 letters from the non-O's so 5C3 x 8C1

v) For this we can do complementary event so total ways minus ways to pick zero L's. Total is just 13C4 and the ways to pick no L's is 10C4 as there are 3 L's so we can pick from 10 letters only. Therefore 13C4 - 10C4

vi) Two L's are chosen at least so there's 2 or 3. For 2 it's 8C2 to pick the remaining O's. For 3 it's just 8C1 to pick the 1 O. Add these to get 8C2 + 8C1

Correct me if I'm wrong, hope this helped.

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