A total of 8 different books are to be distributed among 4 students so that each student receives at least one book. At most 2 of the students are to receive the same number of books, and no two of the remaining students are to receive an equal number of books. What is the least possible number of books needed for distribution?
A. 8
B. 10
C. 12
D. 14
E. 16
Answer A.
Answer:
To find the least possible number of books needed, we need to distribute the books in a way that (...)
Home > GMAT Focus Edition QUANTITATIVE QUESTION > Problem Solving Word Problems > Combinations
Combinations

A total of 8 different books are to be distributed among 4 students so that each student receives at least one book. At most 2 of the students are to receive the same number of books, and no two of the remaining students are to receive an equal number of books. What is the least possible number of books needed for distribution?
31 March, by hurtado claudio 
John has 12 clients, and he wants to use color coding to identify each of them. He can use either a single color or a pair of two different colors to represent a client code. Assuming that switching the order of colors within a pair does not create a different code, what is the minimum number of colors needed for this coding scheme?
30 November 2023, by hurtado claudioCombinatorial model: (N!)/((k!)(Nk)!)

A local bank that has 15 branches uses a twodigit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of twodigit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 15 codes?
21 February 2022, by hurtado claudioGMAT QUANT Problem Solving, Difficulty: 700Level, Combinations, Source: 800 Score, Source: Grockit
A local bank that has 15 branches uses a twodigit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of twodigit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 15 codes?
A. 3
B. 4
C. 5
D. 6
E. 7 
A certain football coach allows his quarterback to call three plays in a row. If the quarterback can choose from 3 passing plays, 4 running plays, and 2 trick plays, how many different arrangements of plays can be run, if the same play can’t be run more than once?
21 February 2022, by hurtado claudioGMAT QUANT Difficulty: 700Level, Combinations, Source: Veritas Prep in Problem Solving (PS)
A certain football coach allows his quarterback to call three plays in a row. If the quarterback can choose from 3 passing plays, 4 running plays, and 2 trick plays, how many different arrangements of plays can be run, if the same play can’t be run more than once?
A. 24
B. 125
C. 243
D. 504
E. 729 
A password to a certain database consists of digits that cannot be repeated. If the password is known to consist of at least 8 digits and it takes 12 seconds to try one combination, what is the amount of time, in minutes, necessary to guarantee access to database?
21 February 2022, by hurtado claudioGMAT QUANT Difficulty: 700Level, Combinations in Problem Solving (PS)
A password to a certain database consists of digits that cannot be repeated. If the password is known to consist of at least 8 digits and it takes 12 seconds to try one combination, what is the amount of time, in minutes, necessary to guarantee access to database?
A. 8!/5
B. 8!/2
C. 8!
D. 10!/2
E. 5/2.10! 
If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5letter code words to the number of 4letter code words?
21 February 2022, by hurtado claudioGMAT QUANT Problem Solving Difficulty: 600700 Level, Combinations
If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5letter code words to the number of 4letter code words?
A. 5 to 4
B. 3 to 2
C. 2 to 1
D. 5 to 1
E. 6 to 1 
In how many ways can 10 different paintings be distributed between two collectors – Dave and Mona – if both collectors should get an even number of paintings? (All paintings should be given away.)
21 February 2022, by hurtado claudioGMAT QUANT Problem Solving level 700, Combinations
In how many ways can 10 different paintings be distributed between two collectors – Dave and Mona – if both collectors should get an even number of paintings? (All paintings should be given away.)
A) 128
B) 256
C) 420
D) 512
E) 1024 
The Simplastic language has only 2 unique vowels and 3 unique consonants. Every noun in Simplastic has the structure CVCVC, where C stands for a consonant and V stands for a vowel. How many different nouns are possible in Simplastic?
19 February 2022, by hurtado claudioGMAT QUANT Difficulty: 700Level, Combinations
The Simplastic language has only 2 unique vowels and 3 unique consonants. Every noun in Simplastic has the structure CVCVC, where C stands for a consonant and V stands for a vowel. How many different nouns are possible in Simplastic?
A. 9
B. 12
C. 36
D. 72
E. 108 
A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible
19 February 2022, by hurtado claudioGMAT QUANT Difficulty: 600700 Level, Combinations
A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?
(A) 3,024
(B) 4,536
(C) 5,040
(D) 9,000
(E) 10,000