a. In how many different ways can the letters of the word "BIOLOGIST" be arranged in such a way that the vowels always come together

b. In how many different ways can the letters of the word "INDISTINGUISHABLE" be arranged?

c. A bag contains 4 white balls, 5 black balls and 6 red balls. In how many ways can 6 balls be drawn from the bag, if at least 2 black balls is to be included in the drawn?

d. In the entrepreneur project competition. You are chief guest of the competition and you have to pick the top 4 paintings out of 10. Since the order is important. In how many different ways of picking the top three entrepreneur projects.