Question

A shipping clerk has to weigh 6 distinct packets. He weighs them 4 at a time, weighing all the possible combinations of the packets from the 6. The average weight of all the weighing combinations is found to be 500 gm. What is the combined weight of all the 6 packets?

Answer 1

Answer:

The average weight of a packet is 500 / 4 = 125.

So the combined weight is 6 * 125 = 750 gm.

Answer 2

Answer:

Combined weight of all the six packets = 750 grams.

Step-by-step explanation:

Given details:

Total packets to be weighed by the shipping clerk = 6

Average weight of the weighing combinations = 500

Solution:

If four packets are taken for measurement at a time from total of 6, then possible combinations are 6C4 = 6! / 4! (6-4)! = 15.

Therefore, total weight measured in this manner = 15 * 500 =  7500

Now, the combined weight (Actual weight) of all 6 packets can be calculated as follows:

Combined weight of 6 = ( 7500* 6/4 ) / 15 =  750 gm