In how many ways vertices of a square can be coloured with 4 distinct colour if rotations are considered to be equivalent, but reflections are distinct ?
A.
65
B.
70
C.
71
D.
None of these
Answer :
70
Solution :
Here in this case condition is similar to formation of necklace i.e.,
$$\left( {n,k} \right) = \frac{1}{n}\sum\limits_{i = 1}^n {{k^{\gcd \left( {n,i} \right)}}} $$
We can use this formula or from the table (you shouldn’t memorize it) required number of ways is 70.
Releted MCQ Question on Algebra >> Permutation and Combination
Releted Question 1
$$^n{C_{r - 1}} = 36,{\,^n}{C_r} = 84$$ and $$^n{C_{r + 1}} = 126,$$ then $$r$$ is:
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated are
Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 ; and then the men select the chairs from amongst the remaining. The number of possible arrangements is