8. Counting and Probability
Middle Years
8.07 Combinations (Enrichment)
Interactive practice questions
Ben has $3$3 shirts: crimson ($C$C), pink ($P$P) and white ($W$W), and $4$4 ties: blue ($B$B), grey ($G$G), red ($R$R) and yellow ($Y$Y).
a
Fill in the array using capital letters to show all the possible outfits Ben could wear.
| Crimson ($C$C) | Pink ($P$P) | White ($W$W) | |
|---|---|---|---|
| Blue ($B$B) | $C$C,$\editable{}$ | $\editable{}$,$B$B | $\editable{}$,$B$B |
| Grey ($G$G) | $C$C,$\editable{}$ | $\editable{}$,$G$G | $W$W,$\editable{}$ |
| Red ($R$R) | $\editable{}$,$R$R | $\editable{}$,$R$R | $W$W,$\editable{}$ |
| Yellow (Y) | $\editable{}$,$Y$Y | $P$P,$\editable{}$ | $\editable{}$,$Y$Y |
b
How many different outfits are possible?
Easy
1min
Evaluate $\nCr{7}{2}$7C2.
Easy
< 1min
Find the value of $\binom{7}{3}$(73).
Easy
1min
Find the value of $\binom{10}{9}$(109).
Easy
< 1min
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