Question

We are given eight rooks, five of which are red and three of which are blue. (a) In how many ways can the eight rooks be placed on an 8-by-8 chessboard so that no two rooks can attack one another? (b) In how many ways can the eight rooks be placed on a 12-by-12 chessboard so that no two rooks can attack one another?

Answer 1

Ans. There are eight wolf 5 are red & 3 blue ___(Q2 8x8 chess board. -_- - A ook moves in either sey or column For the lot look we haue 8x8 = 64 Choices . placing the first rook leares 49 squares not on the game wil or columu where next wol cau be - placed. Placing second rool leares 6x6 = 36 squares not in the now or column of already placed two rooks - Sunlarly 5x5 uru, 3x3, 2X2 il choices for

the next rook &. Sve ole des o4 Заце ие. Таа и с Иte = 64 x чx36x 2 x сx9xчx | sx3) 7 (81) 8х7х6xs) = Sъх 8! с! x3! = Sъхчодро = 2.2 S Z9go (b) « o zx) - Иладw board, For 1st roole 12x12 cuoices possible zul sool 11x11 Choice piveitarly for the next rooke Choices are lox10, 9х9, 8х8 1 1х7, 6x 6, сkѕ. - Total no. of choices possible if s rooks are Цеѕ оw) 3 але bus - 2x2 x1 x1 xlsxle X9 X9 x 8кek1r2x6x6Үr khs S) x 3) = 12х12 x1 x1 xoxoxqх 9 х 8xxxтxxсxx xx xxxxx xxxxx - 616 19059 2 ооо