Question

When six fair coins are tossed simultaneously, in how many of the outcomes will at most three of the coins turn up as heads?

• A. $25$
• B. $41$
• C. $22$
• D. $42$

Answer 1

Answer: (D)

$42$

Total number of coins $=6$

(1) '0' heads $=1$ chance$\left({}^6{C}_0\right)$

(2) '1' heads $=6$ chance$\left({}^6{C}_1\right)$

(3) '2' heads$=15$ chance$\left({}^6{C}_2\right)$

(4) '3' heads$=20$ chance $\left({}^6{C}_3\right)$

Hence total outcome $=42$