Problem Solving

A certain company will issue 4-letter identification codes to all of its employees. The codes will include only the letters A, C, F, H, K, Q and V. If all the letters of each code are distinct, how many such codes are possible?


The correct answer is 840. This question is asking for the number of ordered subgroups we can make out of a larger group. The permutation formula for ordered subgroups

How do you know if a Q is asking for an ordered subgroups??

An identification code should be unique; so the order of the letters matter. In addition, the letters in the code should be unique in other words should appear only once.

Do not look at it as "groups vs sub groups". Check if the order and repetition matter or not

athary wrote:A certain company will issue 4-letter identification codes to all of its employees. The codes will include only the letters A, C, F, H, K, Q and V. If all the letters of each code are distinct, how many such codes are possible?


The correct answer is 840. This question is asking for the number of ordered subgroups we can make out of a larger group. The permutation formula for ordered subgroups

How do you know if a Q is asking for an ordered subgroups??

I think I understand your problem. You mean when to apply Permutation and when Combination?

Thumb Rule-- Whenever Qn. uses words like Arrangement, Distinct, Unique. One must calculate Permutation & when Qn. uses words like Selection, Choose, calculate combination.

In this question, a Code say ACFH will be different than AFCH, hence use permutation only, as arrangement matters.

thanks that really helps!!!