Answer:
(a) there are 13! factorial ways that they could have been assigned seats;
that is 13x12x11x10x9x8x7x6x5x4x3x2z1=6 227 020 800 ways
(b) the tendency of a man sitting next to a woman and a woman sitting next to a man = 7!=7x6x5x4x3x2x1=5 040 ways
(c) all men + 7!= 7x6x7x5x4x3x2x1= 5 040 ways
also all women sat together= 6x5x4x3x2x1=720 ways.
Explanation:
for the siting arrangement we use combination ; where the sitting arrangement does not matter because there is no preference.
Answer:A)13!=6227020800 ways
B)6!×7!=3,628,800ways
C)If the men sit together,=10,080 ways
If the women sits together=1,440ways
Explanation:to arrange 7 men and 6 women randomly in a straight line using permutation is 13p13= 13factorial=13!=13×12×11×10×9×8×7×6×5×4×3×2×1=622702080 ways of arranging them randomly i.e in no specific order.
B) Arranging 7 men and 6Women such that the women and men alternate,let's first assign the women this will require 6! Ways of arranging men,then the first man will have 7ways,next 6 choices,next man will have 5 choices,and so on.so number of ways of arranging men in alternate to women=7 ×6×5×4×3×2×1=5040
So total ways of alternate arrangements=5040×6!=1260×6×5×4×3×2×1=3,628,800ways
C)if men will seat together there will be 7!ways while the women will all seat to their left or to their right(2ways).
So there 7!×2ways=5040×2=10080ways
II) If the women will seat together ,it will be 6!×2=6×5×4×3×2×1×2=1440ways
