Question

If you roll a die three times, how many different sequences are possible?

Answer 1

Hint: Combinations are used if certain objects are to be arranged in such a way that the order of objects, here we will apply the combinations concepts and then will find the resultant required value.

Complete step by step solution:
Combination is used if the certain objects are to be arranged in such a way that the order of objects is not important whereas the permutation is an ordered combination- an act of arranging the objects or numbers in the specific or the favourable order.
Given that when we roll a die once then will have six different possible results and we have to roll the die three times.
So, the possible results would be $ = 6 \times 6 \times 6 = 216 $
This is the required solution.
So, the correct answer is “216”.

Note: In permutations, specific order and arrangement is the most important whereas a combination is used if the certain objects are to be arranged in such a way that the order of objects is not important. The number of the permutations of the “n” objects taken “r” at the time is determined by the formula - $ {}^np{}_r = \dfrac{{n!}}{{(n - r)!}} $ . Use this formula in the problems where the specific favourable arrangement is required. Combinations are used if the certain objects are to be arranged in such a way that the order of objects is not important. $ ^nc{}_r = \dfrac{{n!}}{{r!(n - r)!}} $