Q.

There are 11 players x1,x2,x3,...........x11 in cricket team. Players x1,x2,..............x7 will bat at first seven places and players x8,x9,x10,x11 will bat at last 4 places. Let the number of ways a batting order of 11 players can be made such that x3 does not play at number three, x6 does not play at number 7 and x9 does not play at number 9 be ‘K’. Then the value of  K10 is

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a

6796

b

6626 

c

6726

d

6696

answer is A.

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Detailed Solution

x1x2x3x4x5x6x7|         Leftx8x9x10x11Right

No. of ways in which batsman can be arranged if  x3 does not play at third place and x6 does not play at number 7.
=7!(6!+6!5!) =7×6×5!11×5!   =31×5!
In right side of if  x9 does not play at no 9 then no of ways of arrangement 
 =4!3!=18
Total no of arrangement

=31×5!×18=558×5!=66960

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