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There are 4 candidates for a Chemistry scholarship, 5 for a Mathematical scholarship, and 6 for a Biology scholarship. In how many ways can these scholarships be awarded?

There are 4 candidates for a Chemistry scholarship, 5 for a Mathematical scholarship, and 6 for a Biology scholarship. In how many ways can these scholarships be awarded? Correct Answer 120

Given:

Number of candidates in chemistry = 4

Number of candidates in mathematics = 5

Number of candidates in biology = 6

Concept: /Formula:

Factorial Notation:

Let n be a positive integer. Then, factorial n, denoted n! is defined as :

n! = n × (n - 1) × (n - 2) ... 3 × 2 × 1 

The different arrangements of a given number of things by taking some or all at a time, are called permutations. 

Number of Permutations:

Number of all permutations of n things, taken r at a time, is given by :

nPr = n!/(n - r)!

Combinations:

Each of the different groups or selections which can be formed by taking some or all of a number of objects is called a combination.

Number of Combinations:

The number of all combinations of n things, taken r at a time is :

nCr = n! /(r!) (n - r)!

Calculation:

Scholarships are one per subject

Number of candidates in chemistry = 4

Number of candidates in mathematics = 5

Number of candidates in biology = 6

∴ Required number of ways = 4C1​ × 5C1 ​ × 6C1​ = 4 × 5 × 6 = 120

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