Question

How many outcomes are possible when flipping four coins?

Answer 1

Hint: When four coins are tossed Then, either we get head on first coins and tails on remaining all three coins, or tails on first on and heads on remaining all three coins,
Means, there will be two possibilities for each coin i.e. heads or tails,
Hence, by applying the concept determine the number of ways when all four coins are tossed simultaneously.

Complete step by step solution:
As per data given in the question,
We have to determine the numbers of ways when four coins are tossed.
As, we know that,
When one coin is tossed then there may be the possibility that either we get heads or we get tails.
In a similar way,
So, total number of ways will be H or T i.e. \[2\]
In a same way,
When two coins are tossed, we will get Heads on first coins and tails on second coin, or tail on first coin and head on second coin, or we get head on first coin and head on second coin or tail on first and second coins.
So, number of ways will be HT, HH, TT, TH i.e. $4.$
Similarly,
In a same way,
When four coins are tossed,
Then the possibilities will be,
TTTT, TTTH, TTHT, THTT, HTTT, TTHH, THTH, HTHT, HHTT, THHT, HTTH, THHH, HTHH, HHTH, HHHT, HHHH
Either we get tails on all four coins or will get heads on all four coins.

Note: When one coins are tossed, then either we get heads or tails,
Similarly, when two coins are tossed,
Then either we get heads or tails on first coins or we will get heads and tails on second coins.
Thus, the total number of possibilities will be HH, HT, TH, TT i.e. $4$ ways.
Hence, in same way,
When three coins are tossed, the number of possibilities will be $=8$
HHH, HHT, HTH, HTT, THH, THT, TTH, TTT