Answer: 0.02257
Step-by-step explanation:
Given : Total cards in a deck = 52
Number of ways to select any 5 cards : [tex]^{52}C_5[/tex]
Since , there are total 13 kinds of card (includes Numbers from 2 to 9 and Ace , king, queen and jack).
Of each kind , there are 4 cards.
Number of ways to select three cards in a five card hand of a single kind : [tex]^{4}C_3\times^{48}C_2[/tex]
Number of ways to select three cards in a five card hand of a exactly three of a kind : [tex]13\times^{4}C_3\times^{48}C_2[/tex]
Now , the required probability = [tex]\dfrac{13\times^{4}C_3\times^{48}C_2}{^{52}C_5}[/tex]
[tex]=\dfrac{13\times4\times\dfrac{48!}{2!46!}}{\dfrac{52!}{5!47!}}\\\\\\=\dfrac{58656}{2598960}[/tex]
[tex]=0.022569027611\approx0.02257[/tex]
∴ The probability of being dealt exactly three of a kind (like three kings or three 7’s, etc.) in a five card hand from a deck of 52 cards= 0.02257
