Question

In how many ways can final 11 players be selected from 15 cricket players- a) there is no restriction b) one of them must be included c) one of them who is in bad form must be always be excluded d) twof them being leg spinners one and only one must be included.

Answer 1

total no. of players = 15
no. of players to be chosen = 11

a) no restriction
no of ways to choose 11 guys from 15 = ¹⁵C₁₁

b) one is to b included always⇒ one already selected

so no of guys left to b selected is = 10  out of 14
therefore no of ways = ¹⁴C₁₀

c) one of them always excluded ⇒ he won't b in selection process
 
so no of players left to b chosen = 11 out of 14 ( cause he's not to b count )
therefore no of ways = ¹⁴C₁₁

d) two of either leg spinner must b included ⇒ either A or B (suppose)

so no of guys left to be selected = 10 out of 15-2 = 13 (A and B)
therefore no of ways = ¹³C₁₀ x ²C₁ (as one of either to b chosen) 

hope u'll get it

Answer 2

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