Permutation-Combination

Answer :

Since each desired number is divisible by 5,

so we must have 5 at the unit place.

So, there is 1 way of doing it.
The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9).

So, there are 5 ways of filling the tens place.
The hundreds place can now be filled by any of the remaining 4 digits.

So, there are 4 ways of filling it.
∴ Required number of numbers = (5 x 4 x 1) = 20.

Answer :

Zero or more bananas can be selected in 4 + 1 = 5 ways (0 orange, 1 orange, 2 orange, 3 orange and 4 orange)

similarly apples can be selected in 7 +1 = 8 ways and mangoes in 6 +1 = 7 ways so total number of ways = 5*8*7 = 280

but we included a case of 0 orange, 0 apple and 0 mangoes, so we have to subtract this,

so 280 - 1 = 279 ways

Answer :

First Indians can be seated along the circular table in 4! Ways and now Americans can be seated in 5! Ways. So 4! 5! Ways

Answer :

Every chess match can have three result i.e. win, loss and draw so now of ways = 3*3*3*3 = 81 ways

Answer :

only 4 players to select, so it can be done in 10c4 = 210