"a gamut of" is correct and usable in written English.
It is used to describe a wide range of items, ideas, or emotions. For example, "She experienced a gamut of emotions during the trial."
Along the way, Young & Lost have provided early releases for a gamut of famous names.
He felt a gamut of weaknesses with other boys, even his brother, who died of influenza.
The company makes a gamut of models, using various materials, including polystyrene, leather and wood.
To hear Mr. Navalkar tell it, the Sena's grievances cover a gamut of social ills.
Goldman has tried a gamut of different strategies to fix its blemished image.
The choreography shapeshifts through a gamut of mating, hunting and territorial rituals.
"What I find stimulating is his use of chance to create a gamut of movement".
Just like his convention speech, Trump ran a gamut of emotions from angry to aggravated.
They have been decidedly uneven, running such a gamut of contemporary genres that Banksy began to feel like a collective.
Cooke's design team strains to compensate with spinning sets, flashing lights and a gamut of ripe fart noises.
The King scowls murderously (what story has he been told?) as the Queen runs through a gamut of guesses.
