Q. 11

# A school awarded 42 medals in hockey, 18 in basketball and 23 in cricket. if these medals were bagged by a total of 65 students and only 4 students got medals in all the three sports, how many students received medals in exactly two of the three sports?

Answer :

Given:

- Total number of students = 65

- Medals awarded in Hockey = 42

- Medals awarded n Basketball = 18

- Medals awarded in Cricket = 23

- 4 students got medals in all the three sports.

To Find:

Number of students who received medals in exactly two of the three sports.

Total number of medals = Medals awarded in Hockey + Medals awarded in Basketball + Medals awarded in Cricket

Total number of medals = 42 + 28 + 23

= 83

It is given that 4 students got medals in all the three sports.

Therefore, the number of medals received by those 4 students =

4 × 3 = 12

Now, the number of medals received by the rest of 61 students =

83 – 12 = 71

Among these 61 students, everyone at least received 1 medal.

Therefore, the number of extra medals = 71 – 1 × 61

= 10

Therefore, we can say that 10 students received more than one and less than three medals, or we can say that 10 students received medals in exactly two of three sports.

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Let A = {a, b, c, d}, B = {c, d, e} and C = {d, e, f, g}. Then verify each of the following identities:

(i) A × (B ∩ C) = (A × B) ∩ (A × C)

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