21. In a TV reality show, a contestant is required to clear all five rounds to get into the finals. Find the number of ways a contestant can fail if the results are updated only after a contestant completes all five rounds?
Answers
Step-by-step explanation:
A, B and C are three containers containing the same amount of water.-
C. Bottles
A. Bowl
B. Beaker
1. From which container will the water evaporate first? -
2. From which container will the water evaporate last? -
3. What is your conclusion? -The doctrine of Sufism was based on union with God which can be achieved through love of God, prayers, fasts and rituals without reference to Hindu or Muslims. It stressed that cultivation of religious experience should be based on the direct perception of God.Adjectives of number refer to things that can be counted-even if it is an indefinite amount in the sentence. These are numbers and amounts, both cardinal numbers and ordinal numbers: one, thousand, gallon, first, fifth, etc.
Therefore the total number of ways to fail in the contest is 31 ways.
Given:
A TV reality show consists of 5 rounds in which a contestant should clear all the rounds to win the contest.
To Find:
The number of ways in which a contestant can fail.
Solution:
The given question can be solved as shown below.
W - win and L - Lose
Let us take 5 cases to solve this question.
Case-1: The contestant may not clear even a single round:
⇒ L L L L L
Or
Win 0 rounds out of 5 = ⁵C₀= 1
Number of possibilities of clearing '0' rounds P₀ = 1 way
Case-2: The contestant may clear only the '1' round:
⇒ { W L L L L ; L W L L L ; L L W L L ; L L L W L ; L L L L W }
Or
Win 1 rounds out of 5 = ⁵C₁ = 5
Number of possibilities of clearing 1 round P₁ = 5 ways
Case-3: The contestant may clear 2 rounds:
⇒ { W W L L L; W L W L L; W L L W L; W L L L W; L W W L L; L W L W L; L W L L W; L L W W L; L L W L W; L L L W W }
Or
Wining 2 rounds out of 5 = ⁵C₂ = ( 5 × 4 ) / 2 = 10
Number of possibilities of clearing 2 round P₂ = 10 ways
Case-4: The contestant may clear 3 rounds:
⇒ { W W W L L; W W L W L; W W L L W; W L W W L; W L W L W; W L L W W; L W W W L; L W L W W; L W W L W; L L W W W }
Or
Win 3 rounds out of 5 = ⁵C₃ = 10
Number of possibilities of clearing 3 rounds P₃ = 10 ways
Case-5: The contestant may clear 4 rounds:
⇒ { W W W W L; W W W L W; W W L W W; W L W W W; L W W W W }
Or
Win 4 rounds out of 5 = ⁵C₄ = 5
Number of possibilities of clearing 4 rounds P₄ = 5 ways
Total number of ways to fail the contest = P₀ + P₁ + P₂ + P₃ + P₄ = 1 + 5 + 10 + 10 + 5 = 31 ways.
Therefore the total number of ways to fail in the contest is 31 ways.
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