B3 Alpine Expedition has 420 kg of luggage.

A What is the minimum number of porters they need to hire if each porter can carry a maximum of 35 kg of load?

B On average, how much weight should each porter carry if there are 15 of them?

C In how many ways can the first three porters choose their loads if they are choosing from ten different loads?

D One of the loads is in the shape of a cuboid, and the other is in the shape of a cylinder with a diameter of $1 \mathrm{~m}$ and a height of $0.8 \mathrm{~m}$. The cuboid is $1.57 \mathrm{~m}$ long and $4 \mathrm{dm}$ wide. How high is it if both loads have the same volume?
B3. At least $\frac{420 \mathrm{~kg}}{35 \mathrm{~kg}}=12$ carriers must be hired.

If there were 15, each carrier would have to carry an average load of $\frac{420 \mathrm{~kg}}{15}=28 \mathrm{~kg}$.

The carriers can choose their load in $10 \cdot 9 \cdot 8=720$ ways.

The volume of the cylinder is calculated using the formula $V=\pi r^{2} v$, where $r=0.5 \mathrm{~m}$ and $v=0.8 \mathrm{~m}$. The volume of the cylinder is $0.628 \mathrm{~m}^{3}$.

The height of the cuboid with a given length and width, given the known volume, is calculated from the equation $v=\frac{V}{a b}=$ $\frac{0.628 \mathrm{~m}^{3}}{1.57 \mathrm{~m} \cdot 0.4 \mathrm{~m}}=1 \mathrm{~m}$.

A Answer, e.g.: At least 12 carriers must be hired. 1 point

B Answer, e.g.: If there were 15 carriers, each would have to carry an average of $28 \mathrm{~kg}$ of load... 1 point

C Answer, e.g.: Three carriers can choose their load in 720 different ways. 2 points

D Calculated volume of the cylinder $V=0.628 \mathrm{~m}^{3} \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots$ Calculated height of the cuboid $v=1 \mathrm{~m}$ 2 points