In how many ways can final 11 players be selected from 15 cricket players- a) there is no restriction b) - Maths - Permutations and Combinations

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

Piyush Garg · Accepted Answer

11 players can be selected out of 15 in
15C11 ways = 15C4 = (15
14 13 12) / (1 2 3 4) = 1365 ways
Since a particular player must be included, we have to select
10 more out of remaining 14 players This can be done in
14C10 = 14C4 = (14 13
12 11)/(1 2 3 4) = 1001 ways
Since a particular player must be always excluded, we have to
choose 11 players out of remaining 14 This can be done
in14C11 ways = 14C3 =
(14 13 12)/(1 2 3) = 364 ways
One leg spinner can be chosen out of 2 in² C1 =
2 ways Then we have to select 10 more players out of 13 (because
second leg spinner can't be included) This can be done
in13C10 ways = 13C3 =
(13 12 11)/(1 2 3) = 286 ways Thus required number of combinations
= 2×286 = 572

hope it got it correct

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.

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.