a commitee prepared a list of twenty players each in test, ODI, t20 cricket tournaments, out of 39 players. three players are there who r in test and ODI list but not in T20. four players are there who r in test and T20 list but not in ODI and same number of players are there who r in all the three lists.

- how many players are there who r exactly in one list?
- how many players sre there who r exactly in two lists?
- how many players are there who r in atleast two lists?
- how many players are there who r in atmost two lists?
- how many players are there who r in ODI and T20 list but not in test lists?

Let test, one-day and t-20 be represented by A, B and C respectively.

Also let *x* be the number of players who are in one day and T-20 but not in test.

Here, *n*(A) = *n*(B) = *n*(C) = 20.

Now,

(1) Number of players only for test matches = 20 – (4 + 4 + 3) = 9

Number of players only for one-day matches = 20 – (3 + 4 + 6) = 7

Number of players only for T-20 matches = 20 – (4 + 4 + 6) = 6

Number of players who are exactly in one list = 9 + 7 + 6 = 22

(2) Number of players who are exactly in two lists = 3 + 4 + 6 = 13

(3) Number of players who are in atleast two lists = Number of players who are exactly in two lists + Number of players who are in all lists = 13 + 4 = 17

(4) Number of players who are in atmost two lists = Number of players who are exactly in one list + Number of players who are exactly in two lists = 22 + 13 = 35

(5) Number of players who are in ODI and T-20 list, but not in test lists = *x* = 6.

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