In a class of 10 students there are 3 girls students. The number of ways in which they can be arranged in a row, so that no two girls are consecutive is k(8!), then k is equal to

Seven boys can be arranged in 7! ways. If XB1XB2XB3XB4XB5XB6XB7Xs one such arrangement, then 3 girls can be arranged at any of the 3 places marked with a X.  the number of arrangements is  8P3(7!)=(6×7)(8!)=(42)(8!) Thus, K = 42.