From a group of 7 batsmen and 6 bowlers,10 pl | vedclass

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Question

(B) Total players to be selected = $10$.Given: $1$ batsman (captain) and $1$ bowler (vice-captain) are already selected.Remaining players to be select

Vedclass · Accepted Answer

$155$

Vedclass · Answer

(B) Total players to be selected = $10$.Given: $1$ batsman (captain) and $1$ bowler (vice-captain) are already selected.Remaining players to be selected = $10 - 2 = 8$.Remaining pool: $6$ batsmen and $5$ bowlers.Conditions: At least $4$ batsmen and $4$ bowlers in total.Since $1$ batsman and $1$ bowler are already in,we need at least $3$ more batsmen and $3$ more bowlers from the remaining $8$ spots.Possible cases for selecting $8$ players from $6$ batsmen and $5$ bowlers:Case $1$: $5$ batsmen and $3$ bowlers: ${}^6C_5 	imes {}^5C_3 = 6 	imes 10 = 60$.Case $2$: $4$ batsmen and $4$ bowlers: ${}^6C_4 	imes {}^5C_4 = 15 	imes 5 = 75$.Case $3$: $3$ batsmen and $5$ bowlers: ${}^6C_3 	imes {}^5C_5 = 20 	imes 1 = 20$.Total ways = $60 + 75 + 20 = 155$.

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