Question

1: How many possible outcomes are there if you 3 times in a row either roll a die or flip a coin each time? 

2: How many different outcomes are there if 3 numbers are drawn in sequence out of a bucket containing the numbers 0 -9?

3: How many possibilities are there for 3 consecutive rolls of a die without two consecutive rolls leading to the same number ?

Answer 1

1. Let R be rolling a die. and C be flipping a coin There are R1 to R6 , six outcomes of rolling a die.

There are C1 and C2 , two outcomes of a coin

Thus in all there are 6 + 2 , 8 outcomes in every attempt

Hence, there will be 8 x 8 x 8 = 512 outcomes in 3 times of rolling a die or flipping a coin

Answer : 512

2. Bucket contains numbers 0-9, that is, total 10 numbers

     3 numbers can be drawn in a sequence in ¹⁰C₃ = 120 ways

    Answer : 120

3.  For two consecutive rolls not to be the same,

    one roll can have 6 possibilities, and other two rolls can have 5 possibilities each

   Thus number of possibilities in 3 rolls such that 2 consecutive rolls are not the same = 6 x 5 x 5 = 150

   Answer : 150