a standard deck of 52 playing cards contains 13 cards in each of four suits: hearts, diamonds, clubs, and…

Explanation:

Step1: Calculate number of ways to choose 3 diamonds

The number of ways to choose 3 diamonds out of 13 is given by the combination formula $C(n,k)=\frac{n!}{k!(n - k)!}$, where $n = 13$ (number of diamonds) and $k=3$. $C(13,3)=\frac{13!}{3!(13 - 3)!}=\frac{13\times12\times11}{3\times2\times1}=286$

Step2: Calculate number of ways to choose 1 non - diamond

The number of non - diamonds is $52-13 = 39$. The number of ways to choose 1 non - diamond out of 39 is $C(39,1)=\frac{39!}{1!(39 - 1)!}=39$

Step3: Calculate number of ways to choose 4 cards from 52

The number of ways to choose 4 cards from 52 is $C(52,4)=\frac{52!}{4!(52 - 4)!}=\frac{52\times51\times50\times49}{4\times3\times2\times1}=270725$

Step4: Calculate probability

The number of ways to get exactly 3 diamonds is the product of the number of ways to choose 3 diamonds and the number of ways to choose 1 non - diamond, i.e., $286\times39 = 11154$. The probability $P=\frac{11154}{270725}\approx0.0412\approx4%$

Answer:

4%