kyotsu-test 2017 QCourse2-I-Q2

kyotsu-test · Japan · eju-math__session1 Permutations & Arrangements Selection and Task Assignment
We have four white cards, three red cards and three black cards. A different number is written on each of the ten cards.
(1) Choose two of the ten cards and put one in box A, and one in box B. There are $\mathbf{NO}$ ways of putting two cards in the two boxes.
(2) There are $\mathbf { P Q }$ ways of choosing two cards of the same color, and $\mathbf { R S }$ ways of choosing two cards of different colors.
Next, put the ten cards in a box and take out one card and without returning it to the box, take out second card.
(3) The probability that the two cards taken out have the same color is $\square\mathbf{T UV}$
(4) The probability that the color of the first card taken out is white or red, and the color of the second card taken out is red or black is $\frac { \mathbf { W X } } { \mathbf { Y } \mathbf { Y } }$.
We have four white cards, three red cards and three black cards. A different number is written on each of the ten cards.

(1) Choose two of the ten cards and put one in box A, and one in box B. There are $\mathbf{NO}$ ways of putting two cards in the two boxes.

(2) There are $\mathbf { P Q }$ ways of choosing two cards of the same color, and $\mathbf { R S }$ ways of choosing two cards of different colors.

Next, put the ten cards in a box and take out one card and without returning it to the box, take out second card.

(3) The probability that the two cards taken out have the same color is $\square\mathbf{T UV}$

(4) The probability that the color of the first card taken out is white or red, and the color of the second card taken out is red or black is $\frac { \mathbf { W X } } { \mathbf { Y } \mathbf { Y } }$.