Question

A delicatessen makes a roast beef-on-sourdough sandwich for which you can choose from 9 condiments.

Answer 1

• The number of sandwiches that can be made is : 512
• The minimum number of condiments to offer atleast 2000 different sandwiches is 11

Given that the number of condiments to choose from = 9

The number of arrangements of n items in a list can be obtained using the relation

${2}^{n}$

Here, n = 9

Therefore, the Number of sandwiches that can be made is :

${2}^{9} = 512$

The minimum number of condiments required in other to offer atleast 2000 different sandwiches :

This can be attained thus :

${2}^{n} \geqslant 2000$

n = 11

${2}^{11} = 2048$

Since 2^11 satisfies the inequality, then number of condiments to offer atleast 2000 different sandwiches is 11

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