Question

26. A mathematics department has ten faculty members but only nine offices, so one office must be shared by two individuals. In how many different ways can the offices be assigned?

Answer 1

The different ways can the offices be assigned will be 36.

What is the combination?

The arrangement of the different things or numbers in a number of ways is called the combination.

It is given that:-

• A mathematics department has ten faculty members
• only nine offices, so one office must be shared by two individuals

The number of the different ways are:-

$^9C_2=\dfrac{9!}{(9-2)! \times 2!}$

$^9C_2=\dfrac{9!}{(7)! \times 2!}$

$^9C_2=\dfrac{9\times 8 \times 7!}{(7)! \times 2!}$

$^9C_2=\dfrac{9 \times 8} 2}\ =36$

Therefore the different ways can the offices be assigned will be 36.

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https://brainly.com/question/11732255

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