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?
Given:
- Total number of students $=65$
- Medals awarded in Hockey $=42$
- Medals awarded $\mathrm{n}$ 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 $=4 \times 3=12$
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 $=71-1 \times 61=10$
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.