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IMPORTANT
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How many ways can the word MATHEMATICS be partitioned so that each part contains at least one vowel? For example, MA-THE-MATICS, MATHE-MATICS, MATHEM-A-TICS, and MATHEMATICS are such partitions.

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Important Questions on Counting

HARD
IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 3 - Counting>EXERCISE>Q 1
A telephone number has the form ABC-DEF-GHIJ, where each letter represents a different digit. The digits in each part of the numbers are in decreasing order; that is, A>B>C, D>E>F, and G>H>I>J. Furthermore, D, E, and F are consecutive even digits; G, H, I, and J are consecutive odd digits; and A+B+C=9. Find A.
EASY
IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 3 - Counting>EXERCISE>Q 2
Define na! for n and a positive to be na!=nn-an-2an-3a…..n-ka, where k is the greatest integer for which n>ka. Then the quotient 728!182! is equal to 2x. Find x
MEDIUM
IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 3 - Counting>EXERCISE>Q 3
How many ways can a student schedule 3 mathematics courses - algebra, geometry, and number theory in a 6-period day if no two mathematics courses can be taken in consecutive periods? (What courses the student takes during the other 3 periods is of no concern here).
HARD
IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 3 - Counting>EXERCISE>Q 4
There are 20 students participating in an after-school program offering classes in yoga, bridge, and painting. Each student must take at least one of these three classes, but may take two or all three. There are 10 students taking yoga, 13 taking bridge, and 9 taking painting. There are 9 students taking at least two classes. How many students are taking all three classes?
MEDIUM
IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 3 - Counting>EXERCISE>Q 5
Five friends sat in a movie theater in a row containing 5 seats, numbered 1 to 5 from left to right. (The directions "left" and "right" are from the point of view of the people as they sit in the seats.) During the movie Asha went to the lobby to get some popcorn. When she returned, she found that Bhawna had moved two seats to the right, Chetna had moved one seat to the left, and Divya and Esha had switched seats, leaving an end seat for Asha. In which seat had Asha been sitting before she got up?
EASY
IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 3 - Counting>EXERCISE>Q 6
A palindrome number is the same either read from left to right or right to left, for example. 121 is a palindrome number. Total possible 5-digit palindrome numbers can be written as 10a. Find the value of a
EASY
IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 3 - Counting>EXERCISE>Q 7
Five students A, B, C, D and E form a team to take part in a 5-leg relay competition. If A cannot run the first leg and D cannot run the last leg, how many ways can we arrange them to run the relay?
MEDIUM
IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 3 - Counting>EXERCISE>Q 8
Different positive 3-digit integers are formed from the five digits 1, 2, 3, 5, 7, and repetitions of the digits are allowed. As an example, such positive 3-digit integers include 352, 577, 111, etc. Now, the sum of all the distinct positive 3-digit integers formed in this way is written as ABC50. Find A+B+C.