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MATH / In BINGO, a 5×5 card is filled by marking the middle square as WILD and placing 24 other numbers in the remaining 24 squares. Specifically a card is made by placing 5 numbers from …

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problem

In BINGO, a 5×55\times5 card is filled by marking the middle square as WILD and placing 24 other numbers in the remaining 24 squares. Specifically a card is made by placing 5 numbers from the set 1−151-15 in the first column, 5 numbers from 16−3016-30 in the second column, 4 numbers 31−4531-45 in the third column (skipping the WILD square in the middle), 5 numbers from 46−6046-60 in the fourth column and 5 numbers from 61−7561-75 in the last column. One possible BINGO card is: [asy] for (int i=0; i<6;++i) { draw((i,0)--(i,5)); draw((0,i)--(5,i)); } label("11",(.5,0.5)); label("22",(.5,1.5)); label("33",(.5,2.5)); label("44",(.5,3.5)); label("55",(.5,4.5)); label("2020",(1.5,0.5)); label("1919",(1.5,1.5)); label("1818",(1.5,2.5)); label("1717",(1.5,3.5)); label("1616",(1.5,4.5)); label("3131",(2.5,0.5)); label("3232",(2.5,1.5)); label("Wild",(2.5,2.5)); label("3434",(2.5,3.5)); label("3535",(2.5,4.5)); label("5050",(3.5,0.5)); label("4949",(3.5,1.5)); label("4848",(3.5,2.5)); label("4747",(3.5,3.5)); label("4646",(3.5,4.5)); label("7171",(4.5,0.5)); label("7272",(4.5,1.5)); label("7373",(4.5,2.5)); label("7474",(4.5,3.5)); label("7575",(4.5,4.5)); [/asy] To play BINGO, someone names numbers, chosen at random, and players mark those numbers on their cards. A player wins when he marks 5 in a row, horizontally, vertically, or diagonally. How many distinct possibilities are there for the values in the diagonal going from top left to bottom right of a BINGO card, in order?
Plain-text mathematical notation (without MathML)
In BINGO, a 5×5 card is filled by marking the middle square as WILD and placing 24 other numbers in the remaining 24 squares.


Specifically a card is made by placing 5 numbers from the set 1−15 in the first column, 5 numbers from 16−30 in the second column, 4 numbers 31−45 in the third column (skipping the WILD square in the middle), 5 numbers from 46−60 in the fourth column and 5 numbers from 61−75 in the last column.

One possible BINGO card is:

[asy]
for (int i=0; i<6;++i) {
draw((i,0)--(i,5));
draw((0,i)--(5,i));
}
label("1",(.5,0.5));
label("2",(.5,1.5));
label("3",(.5,2.5));
label("4",(.5,3.5));
label("5",(.5,4.5));

label("20",(1.5,0.5));
label("19",(1.5,1.5));
label("18",(1.5,2.5));
label("17",(1.5,3.5));
label("16",(1.5,4.5));

label("31",(2.5,0.5));
label("32",(2.5,1.5));
label("Wild",(2.5,2.5));
label("34",(2.5,3.5));
label("35",(2.5,4.5));

label("50",(3.5,0.5));
label("49",(3.5,1.5));
label("48",(3.5,2.5));
label("47",(3.5,3.5));
label("46",(3.5,4.5));

label("71",(4.5,0.5));
label("72",(4.5,1.5));
label("73",(4.5,2.5));
label("74",(4.5,3.5));
label("75",(4.5,4.5));

[/asy]

To play BINGO, someone names numbers, chosen at random, and players mark those numbers on their cards.  A player wins when he marks 5 in a row, horizontally, vertically, or diagonally.

How many distinct possibilities are there for the values in the diagonal going from top left to bottom right of a BINGO card, in order?
Original LaTeX notation
In BINGO, a $5\times5$ card is filled by marking the middle square as WILD and placing 24 other numbers in the remaining 24 squares.


Specifically a card is made by placing 5 numbers from the set $1-15$ in the first column, 5 numbers from $16-30$ in the second column, 4 numbers $31-45$ in the third column (skipping the WILD square in the middle), 5 numbers from $46-60$ in the fourth column and 5 numbers from $61-75$ in the last column.

One possible BINGO card is:

[asy]
for (int i=0; i<6;++i) {
draw((i,0)--(i,5));
draw((0,i)--(5,i));
}
label("$1$",(.5,0.5));
label("$2$",(.5,1.5));
label("$3$",(.5,2.5));
label("$4$",(.5,3.5));
label("$5$",(.5,4.5));

label("$20$",(1.5,0.5));
label("$19$",(1.5,1.5));
label("$18$",(1.5,2.5));
label("$17$",(1.5,3.5));
label("$16$",(1.5,4.5));

label("$31$",(2.5,0.5));
label("$32$",(2.5,1.5));
label("Wild",(2.5,2.5));
label("$34$",(2.5,3.5));
label("$35$",(2.5,4.5));

label("$50$",(3.5,0.5));
label("$49$",(3.5,1.5));
label("$48$",(3.5,2.5));
label("$47$",(3.5,3.5));
label("$46$",(3.5,4.5));

label("$71$",(4.5,0.5));
label("$72$",(4.5,1.5));
label("$73$",(4.5,2.5));
label("$74$",(4.5,3.5));
label("$75$",(4.5,4.5));

[/asy]

To play BINGO, someone names numbers, chosen at random, and players mark those numbers on their cards.  A player wins when he marks 5 in a row, horizontally, vertically, or diagonally.

How many distinct possibilities are there for the values in the diagonal going from top left to bottom right of a BINGO card, in order?

level

Level 5

type

Prealgebra

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Source and history

task_id
c09e76b8-2701-52b8-b9b1-a8004ff353e8
task_key
prealgebra--test--c09e76b8-2701-52b8-b9b1-a8004ff353e8
task_revision_id
1
config / split
prealgebra / test

Official source

initial import