Permutation and Combination MCQs

A family consist of a grandfather, 5 sons and daughter and 8 grandchildren. They are to be seated in a row for dinner. The grandchildren wish to occupy the 4 seats at each end and the grandfather refuses to have a grandchild on either side of him. The number of ways in which the family can be made to sit is:

If the letters of the word CHASM are rearranged to form 5 letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word CHASM?

In how many ways can 5 different toys be packed in 3 identical boxes such that no box is empty, if any of the boxes may hold all of the toys?

What is the value of 1 × 1! + 2 × 2! + 3 × 3! + . . . . . . . . n × n! where n! means n factorial or n(n-1) (n-2) . . . . . . . . 1

When six fair coins are tossed simultaneously, in how many of the outcomes will at most three of the coins turn up as heads?

A college has 10 basketball players. A 5 member's team and a captain will be selected out of these 10 players. How many different selections can be made?

How many four letter distinct initials can be formed using the alphabets of English language such that the last of the four words is always a consonant?

What is the total number of ways in which Dishu can distribute 9 distinct gifts among his 8 distinct girlfriends such that each of them gets at least one gift?

How many number of times will the digit 7 be written when listing the integers from 1 to 1000?