Respuesta :
Answer with explanation:
Total number of different candidates who are playing the game=7
Suppose, Seven candidates are represented by ={A,B,C,D,E,F,G}
Total Possible Outcome =7
→Probability that , "A" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{7}[/tex]
→Now, 6 candidates are left.
Probability that , "B" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{6}[/tex]
→Now, 5, candidates are left.
Probability that , "C" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{5}[/tex]
→Now, 4 candidates are left.
Probability that , "D" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{4}[/tex]
→Now, 3 candidates are left.
Probability that , "E" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{3}[/tex]
→Now, 2 candidates are left.
Probability that , "F" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{2}[/tex]
→Now, a single candidates is left.
Probability that , "G" gets his scrap of paper , means the paper on which he or she has written his or her name
[tex]=\frac{\text{total favorable outcome}}{\text{total favorable outcome}}\\\\=\frac{1}{1}=1[/tex]
Required Probability
[tex]=\frac{1}{7} \times\frac{1}{6} \times\frac{1}{5} \times\frac{1}{4} \times\frac{1}{3} \times\frac{1}{2} \times 1\\\\=\frac{1}{5040}[/tex]
