30 identical candies are distributed among 4 students `S_1,S_2,S_3 and S_4`. `S_2` can get at least 4 and at most 7. `S_3` can get at least 2 and at most 6. No restrictions on `S_1 and S_4`. Then number of ways in which the candies can be distributed are _____

In how many ways can 20 identical toys be distributed among 4 children so that each one gets at least 3 toys?

Find the number of ways in which 8 non- identical apples can be distributed among 3 boys such that every boy should get at least 1 apple and at most 4 apples.

The number of ways of disturbing 10 different books among 4 students (S_(1)-S_(4)) such that S_(1) and S_(2) gets 2 books and S_(3) and S_(4) get 3 books each is:

Distribute 12 similar mangoes among 4 children (alpha,beta,gamma,delta) such that alpha gets at least 1mango,beta gets at least 2 mango s,gamma gets at least 2 mangos and delta gets at least 1 mangos.

In an examination, six subjects - S1, S2, S3, S4, S5, and S6 have equal maximum marks. The number of marks scored by one particular candidate in subject S1 is 20% less than his marks in subject S6. The ratio of marks scored by the same candidate in subject S2 to that in S3 is 4: 5 and that in S4 to S5 is 3: 4. The number of marks scored by this candidate in subject S5 is 25% more than that of S6. He scored 65 marks in the subject S3. He scored 436/9 % in the examination and the average of marks scored by him in all the subjects is 218/3 The number of marks obtained by the candidate in the subject S2 was how much less than in the subject S4?

In an examination, six subjects - S1, S2, S3, S4, S5, and S6 have equal maximum marks. The number of marks scored by one particular candidate in subject S1 is 20% less than his marks in subject S6. The ratio of marks scored by the same candidate in subject S2 to that in S3 is 4: 5 and that in S4 to S5 is 3: 4. The number of marks scored by this candidate in subject S5 is 25% more than that of S6. He scored 65 marks in the subject S3. He scored 436/9 % in the examination and the average of marks scored by him in all the subjects is 218/3 Total marks scored by S2 and S3 is multiple of which of the following pairs.

Four bodies of specific heats s_1,s_2,s_3 and s_4 are cooled in the same surroundings. If s_2 gt s_2 gt s_3 gt s_4 , and temperature of all the four bodies is the same, then the specific heat of body which cools fastest, will be –

Sixteen players S_(1) , S_(2) , S_(3) ,…, S_(16) play in a tournament. Number of ways in which they can be grouped into eight pairs so that S_(1) and S_(2) are in different groups, is equal to

In a conference 10 speakers are present . If S_1 wants to speak before S_2 and S_2 wants to speak after S_3 , then the number of ways all the 10 speakers can give their speeches with the above restriction if the remaining seven speakers have no objection to speak at any number is