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A simpler and equivalent way is the following:

The number of favourable events are:

$$13\times\binom{4}{2}\times\binom{12}{3}\times 4^3=1{,}098{,}240$$

this because:

• you have 13 different ways to chose the pair

• you have $\binom{4}{2}$ different suits for your chosen pair

• you have $\binom{12}{3}$ different triples for the remaining cards

• you have $4^3$ different suits for the remaining cards

A simpler and equivalent way is the following:

The number of favourable events are:

$$13\times\binom{4}{2}\times\binom{12}{3}\times 4^3=1{,}098{,}240$$

this because:

• you have 13 different ways to choose the pair

• you have $\binom{4}{2}$ different suits for your chosen pair

• you have $\binom{12}{3}$ different ways to choose the 3 remaining cards

• you have $4^3$ different suits for the 3 remaining cards

A simpler and equivalent way is the following:

The number of favourable events are:

$$13\times\binom{4}{2}\times\binom{12}{3}\times 4^3=1,098,240$$

this because:

• you have 13 different ways to chose the pair

• you have $\binom{4}{2}$ different suits for your chosen pair

• you have $\binom{12}{3}$ different triples for the remaining cards

• you have $4^3$ different suits for the remaining cards

A simpler and equivalent way is the following:

The number of favourable events are:

$$13\times\binom{4}{2}\times\binom{12}{3}\times 4^3=1{,}098{,}240$$

this because:

• you have 13 different ways to chose the pair

• you have $\binom{4}{2}$ different suits for your chosen pair

• you have $\binom{12}{3}$ different triples for the remaining cards

• you have $4^3$ different suits for the remaining cards

A simpler and equivalent way is the following:

The number of favourable events are:

$$13\times\binom{4}{2}\times\binom{12}{3}\times 4^3=1,098,240$$

this because:

• you have 13 different ways to chose the pair

• you have $\binom{4}{2}$ different suits for you chosen pair

• you have $\binom{12}{3}$ different triples for the remainig cards

• you have $4^3$ different suits for the remainig cards

A simpler and equivalent way is the following:

The number of favourable events are:

$$13\times\binom{4}{2}\times\binom{12}{3}\times 4^3=1,098,240$$

this because:

• you have 13 different ways to chose the pair

• you have $\binom{4}{2}$ different suits for your chosen pair

• you have $\binom{12}{3}$ different triples for the remaining cards

• you have $4^3$ different suits for the remaining cards