A class consists for 30 students, 14 boys and 16 girls. 19. How many ways can a president, a vice president and a secretary be chosen from among them? A. 4 060 B. 1 223 040 C. 24 360 D. 7 338 240
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
A class consists for 30 students, 14 boys and 16 girls.
19. How many ways can a president, a vice president and a secretary be chosen from among them?
A. 4 060
B. 1 223 040
C. 24 360
D. 7 338 240
20. How many ways can 3 students be selected to arrange the chairs in the classroom?
A. 4 060
B. 1 223 040
C. 24 360
D. 7 338 240
It is given that, there are 16 boys and 14 girls in the classroom i.e. total number of students in the classroom =14+16=30
19) No. of ways in which one can choose a president, a vice president and a secretary (i.e. 3 people) be chosen from among them
=30C3 =30!(3!*27!)= 4060
So, (A) is the correct answer.
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