The total number of ways there are for eight blue-shirt and five red-shirt to stand in a line so that no two red-shirts stand next to each other is 609638400.
A permutation of a set is, broadly speaking, a rearranging of its elements if the set is already ordered, or arranging its members into a sequence or linear order.
Given:
The eight blue-shirt and five red-shirt stands in a line,
Calculate the number of ways as shown below,
The total number of ways = Total no of permutations of blue ones × Total permutation of 9 positions, taken 5 at a time,
N = 8! × 9! / (9 - 5)!
N = 40320 × 362880 /24
N = 609638400
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