A collection of questions that typically appear from the topic of Permutation
and Combination.
Question 1: A college has 10 basketball players. A
5-member team and a captain will be selected out of these 10
players. How many different selections can be made?
Explanatory Answer �
Question 2: Badri has 9 pairs of dark Blue socks and 9
pairs of Black socks. He keeps them all in a same bag. If he picks
out three socks at random what is the probability he will get a
matching pair?
Solution �
Question 3: How many words of 4 consonants and 3 vowels
can be made from 12 consonants and 4 vowels, if all the letters are
different?
Solution �
Question 4: 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?
Solution �
Question 5: 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?
Solution �
Question 6: When four fair dice are rolled
simultaneously, in how many outcomes will at least one of the dice
show 3?
Explanatory Answer �
Question 7: In how many ways can the letters of the word
EDUCATION be rearranged so that the relative position of the vowels
and consonants remain the same as in the word EDUCATION?
Solution �
Question 8: How many ways can 10 letters be posted in 5
post boxes, if each of the post boxes can take more than 10 letters?
Solution �
Question 9: A team of 8 students goes on an excursion,
in two cars, of which one can seat 5 and the other only 4. In how
many ways can they travel?
Solution �
Question 10: How many ways can 4 prizes be given away to
3 boys, if each boy is eligible for all the prizes?
Solution �
Question 11: There are 12 yes or no questions. How many
ways can these be answered?
Solution �
Question 12: How many words can be formed by
re-arranging the letters of the word ASCENT such that A and T occupy
the first and last position respectively?
Solution �
Question 13: Four dice are rolled simultaneously. What
is the number of possible outcomes in which at least one of the die
shows 6?
Solution �
Question 14: How many alphabets need to be there in a
language if one were to make 1 million distinct 3 digit initials
using the alphabets of the language?
Solution �
Question 15: In how many ways can the letters of the
word MANAGEMENT be rearranged so that the two As do not appear
together?
Solution �
Question 16: There are 5 Rock songs, 6 Carnatic songs
and 3 Indi pop songs. How many different albums can be formed using
the above repertoire if the albums should contain at least 1 Rock
song and 1 Carnatic song?
Solution �
Question 17: 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
Solution �
Question 18: How many number of times will the digit '7'
be written when listing the integers from 1 to 1000?
Solution �
