Six dice are thrown. The probability that different numbers will tum up is equal to

Question

Six dice are thrown. The probability that different numbers will tum up is equal to (A) (5/36) (B) (5/324) (C) (3/324) (D) (1/324)

Tardigrade Admin · Accepted Answer

When six dice are thrown, the total number of outcomes is 66. They can show up different number in 6p6 = angle 6 ways. ∴ Required probability = (6/66) = (5/65) = (120/6 ×6× 6× 6× 6) = (5/324)

Q. Six dice are thrown. The probability that different numbers will tum up is equal to

$\frac{5}{36}$

$\frac{5}{324}$

$\frac{3}{324}$

$\frac{1}{324}$

When six dice are thrown, the total number of outcomes is $6^{6}$ . They can show up different number in $^{6} p_{6} = ∠ 6$ ways.
$∴$ Required probability $= \frac{6}{6 ^{6}}$
$= \frac{5}{6 ^{5}} = \frac{120}{6 \times 6 \times 6 \times 6 \times 6} = \frac{5}{324}$

Q. Six dice are thrown. The probability that different numbers will tum up is equal to

365​

3245​

3243​

3241​

When six dice are thrown, the total number of outcomes is 66. They can show up different number in 6p6​=∠6 ways. ∴ Required probability =666​ =655​=6×6×6×6×6120​=3245​

$\frac{5}{36}$

$\frac{5}{324}$

$\frac{3}{324}$

$\frac{1}{324}$

When six dice are thrown, the total number of outcomes is $6^{6}$ . They can show up different number in $^{6} p_{6} = ∠ 6$ ways.
$∴$ Required probability $= \frac{6}{6 ^{6}}$
$= \frac{5}{6 ^{5}} = \frac{120}{6 \times 6 \times 6 \times 6 \times 6} = \frac{5}{324}$