Can anyone clear the doubt regarding these 4 scenarios ?

a. Distribution of different objects to different things

b. Distribution of different objects to identical things

c. Distribution of identical objects to different things

d. Distribution of identical objects to identical things

Such kind of scenarios are always confusing and take up a huge amount of time while solving.

How many 4 digit nos exist which are not less than 2000 but not greater than 6000 and which have all digits even or zero

There are 8 horizontal roads and 6 vertical roads so basically we have an option at each corner whether to continue or not so we need to arrange 8 HHHHHHHH and 6 VVVVVV this can be done in 14!/6!8!

In how many ways can 100 soldiers be divided into 4 squads of 10,20,30,40 respectively

1) 1700

2) 18!

3) 190

4) None of these Skip

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In arihant book it is written as 100!/(10! X 20!X 30!X40!). but i feel when we solve using cases , only 38 cases seem to be coming???? Inputs will be appreciated!!!

In how many ways can 100 soldiers be divided into 4 squads of 10,20,30,40 respectively

In how many ways can 12 papers be arranged, if the best and the worst paper never come together ?

How many 6 digit numbers contain exactly 4 different digits ?

I have four lights of red colour, five lights of blue colour, six lights of yellow colour and seven lights of green colour. In how many ways can I signal by using atmost four lights, if a light is necessary for giving a signal?

in how many ways a person can select 5 choclates from an unlimited supply of cadbury dairymilk , 5star and munch ???