In how many ways can 5 identical English books and 3 identical Hindi books be placed in a row so that 2 Hindi books may not be together?

My approach is we have to place them alternatively such as “HEHEHEEE”. So we have total 6 spaces for placing H.

In how many ways can 5 identical English books and 3 identical Hindi books be placed in a row so that 2 Hindi books may not be together?

My approach is we have to place them alternatively such as “HEHEHEEE”. So we have total 6 spaces for placing H.

I don’t understand how you got 6 by pacing them alternately, all I see are these:

HEHEHEEE

EHEHEHEE

EEHEHEHE

EEEHEHEH

Please explain what you mean by “alternatively”

How I would approach this:

Total ways in which we can arrange the books = \frac{8!}{5! * 3!} = 8 * 7 * 2 = 112

The number of ways we can arrange the 3 Hs next to each other:

HHH_ _ _ _ _

_ HHH_ _ _ _

_ _ HHH_ _ _

_ _ _ HHH_ _

_ _ _ _ HHH_

_ _ _ _ _ HHH

6

So, ans 112 - 6 = 106

Thank you for the reply, but I guess you are counting the arrangement where 2 H can be placed next to each other such as “HEHHEEEE”.

I found this question in a testprep book where the solution was 6C3 as there are 6 spaces around 5 E such as “-E-E-E-E-E-”

So, they just filled these 6 spaces using 3 H in 6C3 way which seems incorrect to me.

Oh sorry my bad

The question specifies to not include those, my bad

No, I think the test prep’s method is correct

@abulfatharifat97 did u consider this arrangement?

HEHEEHEE

HEEHEEHE

they don’t have to be placed alternately as we have more spaces than the no of objects to be placed

Yeah, you are right. Total arrangement= 6C3