Correct ans is A and B are independent events.
Vowels = E, E and A. They can be arranged in 3!/2! Ways
So total ways = 6!*(3!/2!) = 2160
Zero or more Cherries can be selected in 4 + 1 = 5 ways (0 cherry, 1 cherry, 2 cherries, 3 cherries and 4 cherries)
Similarly pomegranates can be selected in 7 +1 = 8 ways
And guavas in 6 +1 = 7 ways
So total number of ways = 5*8*7 = 280
But we included a case of 0 cherry, 0 pomegranate and 0 guava, so we have to subtract this, so 280 – 1 = 279 ways
This problem is equivalent to finding the number of 3 digit numbers with distinct digits that can be formed
using the digits 1, 2, 3, 4, 5 and 6.
Now for three digits, the places can be field in 6, 5, and 4 different ways.
4 5 6
Total number of possible dice throws when each shows a distinct face is 4 × 5 × 6 = 120.