SOLUTION: Find the number of ways of permitting the letters of the word HELL, such that: a) The 2l’s will always be together b) The 2l’s will always be apart 2. Given that there are

Question 1160133: Find the number of ways of permitting the letters of the word HELL, such that:
a) The 2l’s will always be together
b) The 2l’s will always be apart
2. Given that there are 10 students to be seated on 5 desks. How many different arrangements of the students are possible on the assumption that all seats are to be filled
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.

I will solve #2 ONLY.

In all, there are 10 seats. (Although the problem does not say it clearly, openly and explicitly, it is clear from the context)


    By the way, it is a HUGE deficiency of the problem (!)
    All essential conditions for the solution MUST be presented in clear form (!)
    A reader should not retrieve them from the context (!) (!) (!)


Then the number of ways is  10*9*8*7*6*5*4*3*2*1 = 10! = 3628800.


EXPLANATION


Any of 10 students can occupy the seat #1.

Any of remaining 9 students may occupy the seat #2.

Any of remaining 8 students may occupy the seat #3.


    . . . And so on, to the end . . . 


It is a standard method and a standard mantra in solving such problems.

Done.

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