kyotsu-test 2010 QCourse1-II-Q1

kyotsu-test · Japan · eju-math__session1 Permutations & Arrangements Forming Numbers with Digit Constraints

Q1 Using the five numerals $0,1,2,3,4$, we are to make four-digit integers. (Note that "0123", etc. are not allowed.)
(1) The total possible number of integers where the digits are all different numerals is $\mathbf{AB}$. Among them, the total number of integers that do not use 0 is $\mathbf{CD}$.
(2) If we are allowed to use the same numeral repeatedly, then the total possible number of four-digit integers is $\mathbf{EFG}$. Among them
(i) the total number of integers that use both 1 and 3 twice is $\mathbf{H}$,
(ii) the total number of integers that use both 0 and 4 twice is $\mathbf{I}$,
(iii) the total number of integers that use both of two numerals twice is $\mathbf{JK}$.

Q1 Using the five numerals $0,1,2,3,4$, we are to make four-digit integers. (Note that "0123", etc. are not allowed.)

(1) The total possible number of integers where the digits are all different numerals is $\mathbf{AB}$. Among them, the total number of integers that do not use 0 is $\mathbf{CD}$.

(2) If we are allowed to use the same numeral repeatedly, then the total possible number of four-digit integers is $\mathbf{EFG}$. Among them

(i) the total number of integers that use both 1 and 3 twice is $\mathbf{H}$,

(ii) the total number of integers that use both 0 and 4 twice is $\mathbf{I}$,

(iii) the total number of integers that use both of two numerals twice is $\mathbf{JK}$.

Paper Questions

QCourse1-I-Q1 QCourse1-I-Q2 QCourse1-II-Q1 QCourse1-II-Q2 QCourse1-III QCourse1-IV QCourse2-I-Q1 QCourse2-I-Q2 QCourse2-II QCourse2-III QCourse2-IV-Q1 QCourse2-IV-Q2